Theorem com25 91

Description: Commutation of antecedents. Swap 2nd and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)

Hypothesis

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

Assertion

Ref	Expression
com25	|- ( ph -> ( ta -> ( ch -> ( th -> ( ps -> et ) ) ) ) )

Proof of Theorem com25

Step	Hyp	Ref	Expression
1		com5.1	. . . 4 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
2	1	com24 87	. . 3 |- ( ph -> ( th -> ( ch -> ( ps -> ( ta -> et ) ) ) ) )
3	2	com45 89	. 2 |- ( ph -> ( th -> ( ch -> ( ta -> ( ps -> et ) ) ) ) )
4	3	com24 87	1 |- ( ph -> ( ta -> ( ch -> ( th -> ( ps -> 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:  bj-inf2vnlem2  14605