Theorem 3anidm12 1306

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 1208	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 579	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  3anidm13  1307  syl2an3an  1309  fovcl  5997  prarloclemarch2  7436  nq02m  7482  recexprlem1ssl  7650  recexprlem1ssu  7651  nncan  8204  dividap  8676  modqid0  10368  sqdividap  10603  subsq  10645  retanclap  11748  tannegap  11754  gcd0id  11998  coprm  12162