Theorem ax3h

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

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

Proof

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