Theorem 19.37imv

Description: One direction of 19.37v that can be proven without ax-6 . (Contributed by Rohan Ridenour, 16-Apr-2022)

	Ref	Expression
Assertion	19.37imv	|- ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		ax-5	|- ( ph -> A. x ph )
2		19.35	|- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
3	2	biimpi	|- ( E. x ( ph -> ps ) -> ( A. x ph -> E. x ps ) )
4	1 3	syl5	|- ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) )