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Theorem 3anidm12 1273
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 1184 . 2  |-  ( ph  ->  ( ( ph  /\  ps )  ->  ch )
)
32anabsi5 568 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 962
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 depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  3anidm13  1274  syl2an3an  1276  prarloclemarch2  7234  nq02m  7280  recexprlem1ssl  7448  recexprlem1ssu  7449  nncan  7998  dividap  8468  modqid0  10130  subsq  10406  retanclap  11436  tannegap  11442  gcd0id  11674  coprm  11829
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