Theorem bj-looinvi 32554

Description: Inference associated with looinv 194. Its associated inference is bj-looinvii 32555. (Contributed by BJ, 30-Mar-2020.)

Hypothesis

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

Assertion

Ref	Expression
bj-looinvi	|- ( ( ps -> ph ) -> ph )

Proof of Theorem bj-looinvi

Step	Hyp	Ref	Expression
1		bj-looinvi.1	. 2 |- ( ( ph -> ps ) -> ps )
2		looinv 194	. 2 |- ( ( ( ph -> ps ) -> ps ) -> ( ( ps -> ph ) -> ph ) )
3	1, 2	ax-mp 5	1 |- ( ( ps -> ph ) -> 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:  bj-looinvii  32555