Theorem com14 87

Description: Commutation of antecedents. Swap 1st and 4th. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)

Hypothesis

Ref	Expression
com4.1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Assertion

Ref	Expression
com14	|- ( th -> ( ps -> ( ch -> ( ph -> ta ) ) ) )

Proof of Theorem com14

Step	Hyp	Ref	Expression
1		com4.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	com4l 83	. 2 |- ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )
3	2	com3r 78	1 |- ( th -> ( ps -> ( ch -> ( ph -> ta ) ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7

This theorem is referenced by:  f1o2ndf1  5869  fz0fzdiffz0  9141  elfzodifsumelfzo  9210  ssfzo12  9233  dfgcd2  10403  cncongr1  10485