Theorem bj-19.36im

Description: One direction of 19.36 from the same axioms as 19.36imv . (Contributed by BJ, 2-Dec-2023)

	Ref	Expression
Assertion	bj-19.36im	|- ( F// x ps -> ( E. x ( ph -> ps ) -> ( A. x ph -> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		19.35	|- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2		bj-nnfe	|- ( F// x ps -> ( E. x ps -> ps ) )
3	2	imim2d	|- ( F// x ps -> ( ( A. x ph -> E. x ps ) -> ( A. x ph -> ps ) ) )
4	1 3	syl5bi	|- ( F// x ps -> ( E. x ( ph -> ps ) -> ( A. x ph -> ps ) ) )