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Theorem 3anidm23 1276
Description: Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)
Hypothesis
Ref Expression
3anidm23.1  |-  ( (
ph  /\  ps  /\  ps )  ->  ch )
Assertion
Ref Expression
3anidm23  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem 3anidm23
StepHypRef Expression
1 3anidm23.1 . . 3  |-  ( (
ph  /\  ps  /\  ps )  ->  ch )
213expa 1182 . 2  |-  ( ( ( ph  /\  ps )  /\  ps )  ->  ch )
32anabss3 575 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 963
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 965
This theorem is referenced by:  efrirr  4279  subeq0  8008  halfaddsub  8974  avglt2  8979  efsub  11415  sinmul  11478  xmet0  12562
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