Theorem com3l 81

Description: Commutation of antecedents. Rotate left. (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
com3l	|- ( ps -> ( ch -> ( ph -> th ) ) )

Proof of Theorem com3l

Step	Hyp	Ref	Expression
1		com3.1	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
2	1	com3r 79	. 2 |- ( ch -> ( ph -> ( ps -> th ) ) )
3	2	com3r 79	1 |- ( ps -> ( ch -> ( ph -> th ) ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  com4l  84  impd  254  3imp231  1228  expdcom  1492  nebidc  2500  sbcimdv  3117  prel12  3896  reusv3  4608  relcoi1  5322  oprabid  6120  poxp  6472  reldmtpos  6529  tfrlem9  6595  tfri3  6643  ordiso2  7381  distrlem5prl  7959  distrlem5pru  7960  bndndx  9573  uzind2  9768  leexp1a  11051  swrdswrdlem  11497  swrdswrd  11498  swrdccat3blem  11532  reuccatpfxs1lem  11539  cncongr1  12905  infpnlem1  13166  gausslemma2dlem1a  16399  uhgr2edg  16669  lealltlt1  16973  bj-inf2vnlem2  17219