Theorem com5l 86

Description: Commutation of antecedents. Rotate left. (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
com5l	|- (ps -> (ch -> (th -> (ta -> (ph -> et)))))

Proof of Theorem com5l

Step	Hyp	Ref	Expression
1		com5.1	. . 3 |- (ph -> (ps -> (ch -> (th -> (ta -> et)))))
2	1	com4l 78	. 2 |- (ps -> (ch -> (th -> (ph -> (ta -> et)))))
3	2	com45 83	1 |- (ps -> (ch -> (th -> (ta -> (ph -> et)))))

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  com15  87  com52l  88  com52r  89