Theorem 3anidm12 1226

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 1141	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 543	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  3anidm13  1227  syl2an3an  1229  prarloclemarch2  6609  nq02m  6655  recexprlem1ssl  6823  recexprlem1ssu  6824  nncan  7337  dividap  7789  modqid0  9352  subsq  9581  gcd0id  10370  coprm  10523