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  4606  relcoi1  5319  oprabid  6117  poxp  6468  reldmtpos  6524  tfrlem9  6590  tfri3  6638  ordiso2  7375  distrlem5prl  7953  distrlem5pru  7954  bndndx  9562  uzind2  9758  leexp1a  11031  swrdswrdlem  11476  swrdswrd  11477  swrdccat3blem  11511  reuccatpfxs1lem  11518  cncongr1  12881  infpnlem1  13138  gausslemma2dlem1a  16177  uhgr2edg  16447  lealltlt1  16751  bj-inf2vnlem2  16997