Theorem 3anidm23 1334

Description: Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)

Hypothesis

Ref	Expression
3anidm23.1	|- ( ( ph /\ ps /\ ps ) -> ch )

Assertion

Ref	Expression
3anidm23	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem 3anidm23

Step	Hyp	Ref	Expression
1		3anidm23.1	. . 3 |- ( ( ph /\ ps /\ ps ) -> ch )
2	1	3expa 1230	. 2 |- ( ( ( ph /\ ps ) /\ ps ) -> ch )
3	2	anabss3 587	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  efrirr  4476  subeq0  8504  halfaddsub  9477  avglt2  9483  efsub  12375  sinmul  12438  pythagtriplem4  12974  pythagtriplem16  12985  ballotfilemfc0  13157  ballotfilemfcc  13158  xmet0  15277