Theorem ax3h 41060

Description: Recovery of ax-3 8 from hirstL-ax3 41059. (Contributed by Jarvin Udandy, 3-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax3h	|- ( ( -. ph -> -. ps ) -> ( ps -> ph ) )

Proof of Theorem ax3h

Step	Hyp	Ref	Expression
1		hirstL-ax3 41059	. 2 |- ( ( -. ph -> -. ps ) -> ( ( -. ph -> ps ) -> ph ) )
2		jarr 106	. 2 |- ( ( ( -. ph -> ps ) -> ph ) -> ( ps -> ph ) )
3	1, 2	syl 17	1 |- ( ( -. ph -> -. ps ) -> ( ps -> ph ) )

Syntax hints:   -. wn 3   -> wi 4

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

This theorem depends on definitions:  df-bi 197  df-or 385

This theorem is referenced by: (None)