Theorem 3anidm23 1240

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 1146	. 2 |- ( ( ( ph /\ ps ) /\ ps ) -> ch )
3	2	anabss3 553	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 927

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

This theorem depends on definitions:  df-bi 116  df-3an 929

This theorem is referenced by:  efrirr  4204  subeq0  7805  halfaddsub  8748  avglt2  8753  efsub  11136  sinmul  11200  xmet0  12165