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Theorem 3anidm12 1227
Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
Hypothesis
Ref Expression
3anidm12.1  |-  ( (
ph  /\  ph  /\  ps )  ->  ch )
Assertion
Ref Expression
3anidm12  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem 3anidm12
StepHypRef Expression
1 3anidm12.1 . . 3  |-  ( (
ph  /\  ph  /\  ps )  ->  ch )
213expib 1142 . 2  |-  ( ph  ->  ( ( ph  /\  ps )  ->  ch )
)
32anabsi5 544 1  |-  ( (
ph  /\  ps )  ->  ch )
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:  3anidm13  1228  syl2an3an  1230  prarloclemarch2  6671  nq02m  6717  recexprlem1ssl  6885  recexprlem1ssu  6886  nncan  7404  dividap  7856  modqid0  9432  subsq  9678  gcd0id  10514  coprm  10667
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