Theorem com35 98

Description: Commutation of antecedents. Swap 3rd and 5th. Deduction associated with com24 95. Double deduction associated with com13 88. (Contributed by Jeff Hankins, 28-Jun-2009.)

Hypothesis

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

Assertion

Ref	Expression
com35	|- ( ph -> ( ps -> ( ta -> ( th -> ( ch -> et ) ) ) ) )

Proof of Theorem com35

Step	Hyp	Ref	Expression
1		com5.1	. . . 4 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
2	1	com34 91	. . 3 |- ( ph -> ( ps -> ( th -> ( ch -> ( ta -> et ) ) ) ) )
3	2	com45 97	. 2 |- ( ph -> ( ps -> ( th -> ( ta -> ( ch -> et ) ) ) ) )
4	3	com34 91	1 |- ( ph -> ( ps -> ( ta -> ( th -> ( ch -> 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:  swrdswrdlem  13459  bcthlem5  23125  nocvxminlem  31893  iccpartigtl  41359  nn0sumshdiglemB  42414