Theorem com34 83

Description: Commutation of antecedents. Swap 3rd and 4th. (Contributed by NM, 25-Apr-1994.)

Hypothesis

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

Assertion

Ref	Expression
com34	|- ( ph -> ( ps -> ( th -> ( ch -> ta ) ) ) )

Proof of Theorem com34

Step	Hyp	Ref	Expression
1		com4.1	. 2 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2		pm2.04 82	. 2 |- ( ( ch -> ( th -> ta ) ) -> ( th -> ( ch -> ta ) ) )
3	1, 2	syl6 33	1 |- ( ph -> ( ps -> ( th -> ( ch -> ta ) ) ) )

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  com35  90  3an1rs  1250  rspct  2922  po2nr  4456  funssres  5423  f1ocnv2d  6297  f1o3d  6301  tfrlem9  6595  nnmass  6765  nnmordi  6794  genpcdl  7892  genpcuu  7893  mulnqprl  7941  mulnqpru  7942  distrlem1prl  7955  distrlem1pru  7956  divgt0  9210  divge0  9211  uzind2  9768  facdiv  11197  swrdswrdlem  11497  wrd2ind  11516  dvdsabseq  12638  divgcdcoprm0  12903  lmodvsdi  14756