Theorem hbe1a

Description: Dual statement of hbe1 . Modified version of axc7e with a universally quantified consequent. (Contributed by Wolf Lammen, 15-Sep-2021)

	Ref	Expression
Assertion	hbe1a	|- ( E. x A. x ph -> A. x ph )

Proof

Step	Hyp	Ref	Expression
1		df-ex	|- ( E. x A. x ph <-> -. A. x -. A. x ph )
2		hbn1	|- ( -. A. x ph -> A. x -. A. x ph )
3	2	con1i	|- ( -. A. x -. A. x ph -> A. x ph )
4	1 3	sylbi	|- ( E. x A. x ph -> A. x ph )