Theorem 3exp 1226

Description: Exportation inference. (Contributed by NM, 30-May-1994.)

Hypothesis

Ref	Expression
3exp.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3exp	|- ( ph -> ( ps -> ( ch -> th ) ) )

Proof of Theorem 3exp

Step	Hyp	Ref	Expression
1		pm3.2an3 1200	. 2 |- ( ph -> ( ps -> ( ch -> ( ph /\ ps /\ ch ) ) ) )
2		3exp.1	. 2 |- ( ( ph /\ ps /\ ch ) -> th )
3	1, 2	syl8 71	1 |- ( ph -> ( ps -> ( ch -> th ) ) )

Syntax hints:   -> wi 4   /\ w3a 1002

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1004

This theorem is referenced by:  3expa  1227  3expb  1228  3expia  1229  3expib  1230  3com23  1233  3an1rs  1243  3exp1  1247  3expd  1248  exp5o  1250  syl3an2  1305  syl3an3  1306  syl2an23an  1333  3impexpbicomi  1482  rexlimdv3a  2650  rabssdv  3304  reupick2  3490  ssorduni  4579  tfisi  4679  fvssunirng  5644  f1oiso2  5957  poxp  6384  tfrlem5  6466  nndi  6640  nnmass  6641  findcard  7058  ac6sfi  7068  mulcanpig  7533  divgt0  9030  divge0  9031  uzind  9569  uzind2  9570  facavg  10980  prodfap0  12072  prodfrecap  12073  fprodabs  12143  dvdsmodexp  12322  dvdsaddre2b  12368  dvdsnprmd  12663  prmndvdsfaclt  12694  fermltl  12772  pceu  12834  mulgass2  14037  islss4  14362  rnglidlmcl  14460  fiinopn  14694  neipsm  14844  tpnei  14850  opnneiid  14854  neibl  15181  tgqioo  15245  gausslemma2dlem1a  15753  ausgrumgrien  15984  ausgrusgrien  15985  usgrausgrben  15986  ushgredgedg  16040  ushgredgedgloop  16042  wlkl1loop  16104