Theorem com25 85

Description: Commutation of antecedents. Swap 2nd and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)

Hypothesis

Ref	Expression
com5.1	|- (ph -> (ps -> (ch -> (th -> (ta -> et)))))

Assertion

Ref	Expression
com25	|- (ph -> (ta -> (ch -> (th -> (ps -> et)))))

Proof of Theorem com25

Step	Hyp	Ref	Expression
1		com5.1	. . . 4 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))
2	1	com24 81	. . 3 |- (ph -> (th -> (ch -> (ps -> (ta -> et)))))
3	2	com45 83	. 2 |- (ph -> (th -> (ch -> (ta -> (ps -> et)))))
4	3	com24 81	1 |- (ph -> (ta -> (ch -> (th -> (ps -> et)))))

Syntax hints:   -> wi 4

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

This theorem is referenced by: (None)