Theorem 3anidm12 1305

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 1207	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 579	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 979

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 981

This theorem is referenced by:  3anidm13  1306  syl2an3an  1308  prarloclemarch2  7431  nq02m  7477  recexprlem1ssl  7645  recexprlem1ssu  7646  nncan  8199  dividap  8671  modqid0  10363  sqdividap  10598  subsq  10640  retanclap  11743  tannegap  11749  gcd0id  11993  coprm  12157