Theorem com13 74

Description: Commutation of antecedents. Swap 1st and 3rd. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)

Hypothesis

Ref	Expression
com3.1	|- (ph -> (ps -> (ch -> th)))

Assertion

Ref	Expression
com13	|- (ch -> (ps -> (ph -> th)))

Proof of Theorem com13

Step	Hyp	Ref	Expression
1		com3.1	. . 3 |- (ph -> (ps -> (ch -> th)))
2	1	com3r 73	. 2 |- (ch -> (ph -> (ps -> th)))
3	2	com23 72	1 |- (ch -> (ps -> (ph -> th)))

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:  com24  81  an13s  778  an31s  781  meredith  1404