Theorem 3exp 1204

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 1178	. 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 980

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 982

This theorem is referenced by:  3expa  1205  3expb  1206  3expia  1207  3expib  1208  3com23  1211  3an1rs  1221  3exp1  1225  3expd  1226  exp5o  1228  syl3an2  1283  syl3an3  1284  syl2an23an  1310  3impexpbicomi  1450  rexlimdv3a  2616  rabssdv  3264  reupick2  3450  ssorduni  4524  tfisi  4624  fvssunirng  5576  f1oiso2  5877  poxp  6299  tfrlem5  6381  nndi  6553  nnmass  6554  findcard  6958  ac6sfi  6968  mulcanpig  7419  divgt0  8916  divge0  8917  uzind  9454  uzind2  9455  facavg  10855  prodfap0  11727  prodfrecap  11728  fprodabs  11798  dvdsmodexp  11977  dvdsaddre2b  12023  dvdsnprmd  12318  prmndvdsfaclt  12349  fermltl  12427  pceu  12489  mulgass2  13690  islss4  14014  rnglidlmcl  14112  fiinopn  14324  neipsm  14474  tpnei  14480  opnneiid  14484  neibl  14811  tgqioo  14875  gausslemma2dlem1a  15383