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  1219  rspct  2836  po2nr  4311  funssres  5260  f1ocnv2d  6078  tfrlem9  6323  nnmass  6491  nnmordi  6520  genpcdl  7521  genpcuu  7522  mulnqprl  7570  mulnqpru  7571  distrlem1prl  7584  distrlem1pru  7585  divgt0  8832  divge0  8833  uzind2  9368  facdiv  10721  dvdsabseq  11856  divgcdcoprm0  12104  lmodvsdi  13407