Theorem bj-looinvii 32555

Description: Inference associated with bj-looinvi 32554. (Contributed by BJ, 30-Mar-2020.)

Hypotheses

Ref	Expression
bj-looinvii.1	|- ( ( ph -> ps ) -> ps )
bj-looinvii.2	|- ( ps -> ph )

Assertion

Ref	Expression
bj-looinvii	|- ph

Proof of Theorem bj-looinvii

Step	Hyp	Ref	Expression
1		bj-looinvii.2	. 2 |- ( ps -> ph )
2		bj-looinvii.1	. . 3 |- ( ( ph -> ps ) -> ps )
3	2	bj-looinvi 32554	. 2 |- ( ( ps -> ph ) -> ph )
4	1, 3	ax-mp 5	1 |- ph

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)