Theorem minimp-ax1

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

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

Proof

Step	Hyp	Ref	Expression
1		minimp-syllsimp	|- ( ( ( ph -> ps ) -> ph ) -> ( ps -> ph ) )
2		minimp-syllsimp	|- ( ( ( ( ph -> ps ) -> ph ) -> ( ps -> ph ) ) -> ( ph -> ( ps -> ph ) ) )
3	1 2	ax-mp	|- ( ph -> ( ps -> ph ) )