Theorem 3anidm12 1336

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 1237	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 585	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1009

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 1011

This theorem is referenced by:  3anidm13  1337  syl2an3an  1339  fovcl  6187  prarloclemarch2  7779  nq02m  7825  recexprlem1ssl  7993  recexprlem1ssu  7994  nncan  8548  dividap  9024  modqid0  10768  sqdividap  11022  subsq  11064  retanclap  12470  tannegap  12476  gcd0id  12737  coprm  12903