Theorem conax1 643

Description: Contrapositive of ax-1 6. (Contributed by BJ, 28-Oct-2023.)

Assertion

Ref	Expression
conax1	|- ( -. ( ph -> ps ) -> -. ps )

Proof of Theorem conax1

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 |- ( ps -> ( ph -> ps ) )
2	1	con3i 622	1 |- ( -. ( ph -> ps ) -> -. ps )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605

This theorem is referenced by:  conax1k  644  nnnotnotr  13872