Theorem com15

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

	Ref	Expression
Hypothesis	com5.1	|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Assertion	com15	|- ( ta -> ( ps -> ( ch -> ( th -> ( ph -> et ) ) ) ) )

Proof

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