Theorem 3expib 1146

Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Hypothesis

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

Assertion

Ref	Expression
3expib	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Proof of Theorem 3expib

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3exp 1142	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	impd 251	1 |- ( ph -> ( ( ps /\ ch ) -> th ) )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 924

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 926

This theorem is referenced by:  3anidm12  1231  mob  2797  eqbrrdva  4606  funimaexglem  5097  fco  5176  f1oiso2  5606  caovimo  5838  smoel2  6068  nnaword  6268  3ecoptocl  6379  sbthlemi10  6673  distrnq0  7016  addassnq0  7019  prcdnql  7041  prcunqu  7042  genpdisj  7080  cauappcvgprlemrnd  7207  caucvgprlemrnd  7230  caucvgprprlemrnd  7258  nn0n0n1ge2b  8824  fzind  8859  icoshft  9405  fzen  9455  iseqcoll  10243  shftuz  10247  mulgcd  11279  ialgcvga  11307  lcmneg  11330