Theorem com45 83

Description: Commutation of antecedents. Swap 4th and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)

Hypothesis

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

Assertion

Ref	Expression
com45	|- (ph -> (ps -> (ch -> (ta -> (th -> et)))))

Proof of Theorem com45

Step	Hyp	Ref	Expression
1		com5.1	. 2 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))
2		pm2.04 76	. 2 |- ((th -> (ta -> et)) -> (ta -> (th -> et)))
3	1, 2	syl8 65	1 |- (ph -> (ps -> (ch -> (ta -> (th -> 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:  com35  84  com25  85  com5l  86