Theorem minimp-ax1 1562

Description: Derivation of ax-1 6 from ax-mp 5 and minimp 1560. (Contributed by BJ, 4-Apr-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
minimp-ax1	|- ( ph -> ( ps -> ph ) )

Proof of Theorem minimp-ax1

Step	Hyp	Ref	Expression
1		minimp-sylsimp 1561	. 2 |- ( ( ( ph -> ps ) -> ph ) -> ( ps -> ph ) )
2		minimp-sylsimp 1561	. 2 |- ( ( ( ( ph -> ps ) -> ph ) -> ( ps -> ph ) ) -> ( ph -> ( ps -> ph ) ) )
3	1, 2	ax-mp 5	1 |- ( ph -> ( ps -> ph ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  minimp-pm2.43  1565