Theorem 3anidm13 883

Description: Inference from idempotent law for conjunction.

Hypothesis

Ref	Expression
3anidm13.1	|- ((ph /\ ps /\ ph) -> ch)

Assertion

Ref	Expression
3anidm13	|- ((ph /\ ps) -> ch)

Proof of Theorem 3anidm13

Step	Hyp	Ref	Expression
1		3anidm13.1	. . 3 |- ((ph /\ ps /\ ph) -> ch)
2	1	3com23 839	. 2 |- ((ph /\ ph /\ ps) -> ch)
3	2	3anidm12 882	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 775

This theorem is referenced by:  subge02t 5677  halfaddsubt 6041  avglet 6044  bccmplt 6962  ioo2bl 7912  grpidinvlem2 8049  hvpncan3t 8911

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 777

Copyright terms: Public domain