Theorem com15 87

Description: Commutation of antecedents. Swap 1st and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.) (Proof shortened by Wolf Lammen, 29-Jul-2012.)

Hypothesis

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

Assertion

Ref	Expression
com15	|- (ta -> (ps -> (ch -> (th -> (ph -> et)))))

Proof of Theorem com15

Step	Hyp	Ref	Expression
1		com5.1	. . 3 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))
2	1	com5l 86	. 2 |- (ps -> (ch -> (th -> (ta -> (ph -> et)))))
3	2	com4r 80	1 |- (ta -> (ps -> (ch -> (th -> (ph -> 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)