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Theorem 3expib 1142
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
StepHypRef Expression
1 3exp.1 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213exp 1138 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32impd 251 1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
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 922
This theorem is referenced by:  3anidm12  1227  mob  2775  eqbrrdva  4527  funimaexglem  5007  fco  5081  f1oiso2  5491  caovimo  5719  smoel2  5946  nnaword  6143  3ecoptocl  6254  distrnq0  6700  addassnq0  6703  prcdnql  6725  prcunqu  6726  genpdisj  6764  cauappcvgprlemrnd  6891  caucvgprlemrnd  6914  caucvgprprlemrnd  6942  nn0n0n1ge2b  8497  fzind  8532  icoshft  9077  fzen  9127  shftuz  9832  mulgcd  10538  ialgcvga  10566  lcmneg  10589
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