Theorem bj-19.37im

Description: One direction of 19.37 from the same axioms as 19.37imv . (Contributed by BJ, 2-Dec-2023)

	Ref	Expression
Assertion	bj-19.37im	|- ( F// x ph -> ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		19.35	|- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2		bj-nnfa	|- ( F// x ph -> ( ph -> A. x ph ) )
3	2	imim1d	|- ( F// x ph -> ( ( A. x ph -> E. x ps ) -> ( ph -> E. x ps ) ) )
4	1 3	syl5bi	|- ( F// x ph -> ( E. x ( ph -> ps ) -> ( ph -> E. x ps ) ) )