Theorem 3anidm12 1192

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 1107	. 2 |- ( ph -> ( ( ph /\ ps ) -> ch ) )
3	2	anabsi5 513	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  3anidm13  1193  prarloclemarch2  6517  nq02m  6563  recexprlem1ssl  6731  recexprlem1ssu  6732  nncan  7240  dividap  7678  subsq  9358