Theorem 3anidm12 1308

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

Step	Hyp	Ref	Expression
1		3anidm12.1	. . 3 |- ( ( ph /\ ph /\ ps ) -> ch )
2	1	3expib 1209	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 579	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  3anidm13  1309  syl2an3an  1311  fovcl  6053  prarloclemarch2  7534  nq02m  7580  recexprlem1ssl  7748  recexprlem1ssu  7749  nncan  8303  dividap  8776  modqid0  10497  sqdividap  10751  subsq  10793  retanclap  12066  tannegap  12072  gcd0id  12333  coprm  12499