Deng's legacy is a story that full of fluctuations. Not so many politicians can overcome 3 career downfalls and obtain supreme power at last. To have a brief understanding on how Deng manage to come to power, I think there are 3 key factors, Deng's skillful ability, decision of founding fathers and defects of Hua's legitimacy and capacity.

​

First of all, Deng proved that he was the only one who capable to lead the reformation. So how was he able to build the base of support? Actually, Deng never lack of support. From 1940s to 1976, Deng's achievement in military, economy had already built up his prestige. In Mao's age, only a few people had knowledge on how to lead economic construction and bureaucracy. Deng Xiaoping, Zhou Enlai and Chen Yun always be considered as the most talented in the Communist Party. After Zhou's death, Deng was the only one succeeded to recover China's economy from destruction of Cultural Revolution. His result made him gained greater popularity than his rival.

The next question that have to solve is why Hua Guofeng failed to defeat Deng in power struggle. As I mentioned above, his legitimacy and ability was challenged by Deng and other CCP's member. Hua was not one of the founding fathers of PRC. The most critical reason led him to be successor of Mao was Mao's support. Though Hua Guofeng ultimately defeated the Gang of Four. But he clearly knew that he had a weak claim on China's leader, he needed more accomplishments to confirm his capacity. To strengthen his legitimacy, Hua suggested "Two Whatever" theory. The statement is "We will resolutely uphold whatever policy decisions Chairman Mao made, and unswervingly follow whatever instructions Chairman Mao gave." Unfortunately, the theory led to an opposite result. Generals and people's belief on Mao had already been totally destroyed in the 10 years disaster. What he suggested created new fear in society. Later on, Deng published a statement of "Actual Practice is the Sole Criterion for Judging Truth" which did a fatal damage on Hua's theory. Beside that, Hua attempted to lead a new movement which aimed for social and economic repair. The movement named as "A Great Leap In Western way". It started from 1977 and stopped in 1978 due to great loss. Hua failure on strengthen his weak claim can explain why he lost his political status in a large extent.

The founding fathers also played a great role in Deng-Hua rivalry. As you mentioned, some moderate wings like Yie Jianying and Wang Dongxing participated Hua's action. Something I want to clarify is many CCP cadres supported Hua on the Purge of the Gang of Four does not mean they supported Hua as a the new leader. In 1976-1978, many CCP principal proponent such as Chen Yun, Yie Jianying, Wang Dongxing pay a lot effort on backing Deng. Not just because of the difference in ability but also related to their revolutionary friendship which developed in the Long March, Sino-Japanese war and Chinese Civil War. It's impossible for Hua to gain founding father's loyalty in a short period.

​

I hope this explanation could be helpful.

Sources:

席宣、金春明；"文化大革命簡史"，中共黨史出版社，2006年

"Resolution on Certain Questions in the History of our Party since the Founding of the People's Republic of China"(1981)