Theorem 3anidm12 1290

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 1201	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 574	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  3anidm13  1291  syl2an3an  1293  prarloclemarch2  7381  nq02m  7427  recexprlem1ssl  7595  recexprlem1ssu  7596  nncan  8148  dividap  8618  modqid0  10306  subsq  10582  retanclap  11685  tannegap  11691  gcd0id  11934  coprm  12098