Theorem axc5c7toc5 34197

Description: Rederivation of ax-c5 34168 from axc5c7 34196. Only propositional calculus is used for the rederivation. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc5c7toc5	|- ( A. x ph -> ph )

Proof of Theorem axc5c7toc5

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 |- ( A. x ph -> ( A. x -. A. x ph -> A. x ph ) )
2		axc5c7 34196	. 2 |- ( ( A. x -. A. x ph -> A. x ph ) -> ph )
3	1, 2	syl 17	1 |- ( A. x ph -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-c5 34168  ax-c7 34170

This theorem is referenced by: (None)