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Theorem 3anidm13 1257
Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
Hypothesis
Ref Expression
3anidm13.1  |-  ( (
ph  /\  ps  /\  ph )  ->  ch )
Assertion
Ref Expression
3anidm13  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem 3anidm13
StepHypRef Expression
1 3anidm13.1 . . 3  |-  ( (
ph  /\  ps  /\  ph )  ->  ch )
213com23 1170 . 2  |-  ( (
ph  /\  ph  /\  ps )  ->  ch )
323anidm12 1256 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 945
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 947
This theorem is referenced by:  ltnsym  7814  npncan2  7953  ltsubpos  8180  leaddle0  8203  subge02  8204  halfaddsub  8905  avglt1  8909
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