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Theorem impac 378
Description: Importation with conjunction in consequent. (Contributed by NM, 9-Aug-1994.)
Hypothesis
Ref Expression
impac.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
impac  |-  ( (
ph  /\  ps )  ->  ( ch  /\  ps ) )

Proof of Theorem impac
StepHypRef Expression
1 impac.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21ancrd 324 . 2  |-  ( ph  ->  ( ps  ->  ( ch  /\  ps ) ) )
32imp 123 1  |-  ( (
ph  /\  ps )  ->  ( ch  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  imdistanri  442  f1elima  5642
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