Theorem com13 80

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 79	. 2 |- ( ch -> ( ph -> ( ps -> th ) ) )
3	2	com23 78	1 |- ( ch -> ( ps -> ( ph -> th ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  com24  87  an13s  567  an31s  570  3imp31  1198  3imp21  1200  funopg  5293  f1o2ndf1  6295  brecop  6693  fiintim  7001  elpq  9740  xnn0lenn0nn0  9957  elfz0ubfz0  10217  elfz0fzfz0  10218  fz0fzelfz0  10219  fz0fzdiffz0  10222  fzo1fzo0n0  10276  elfzodifsumelfzo  10294  ssfzo12  10317  ssfzo12bi  10318  facwordi  10849  fihashf1rn  10897  oddnn02np1  12062  oddge22np1  12063  evennn02n  12064  evennn2n  12065  dfgcd2  12206  sqrt2irr  12355  lmodfopnelem1  13956  mpomulcn  14886  zabsle1  15324  gausslemma2dlem1a  15383  2lgsoddprm  15438  bj-inf2vnlem2  15701