Theorem 3anidm23 1228

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 1138	. 2 |- ( ( ( ph /\ ps ) /\ ps ) -> ch )
3	2	anabss3 549	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:  efrirr  4108  subeq0  7334  halfaddsub  8265  avglt2  8270