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 ) ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  com4l  84  com35  90  3an1rs  1243  rspct  2901  po2nr  4404  funssres  5366  f1ocnv2d  6222  tfrlem9  6480  nnmass  6650  nnmordi  6679  genpcdl  7729  genpcuu  7730  mulnqprl  7778  mulnqpru  7779  distrlem1prl  7792  distrlem1pru  7793  divgt0  9042  divge0  9043  uzind2  9582  facdiv  10990  swrdswrdlem  11275  wrd2ind  11294  dvdsabseq  12398  divgcdcoprm0  12663  lmodvsdi  14315