Theorem 3anidm13 1227

Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)

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 1144	. 2 |- ( ( ph /\ ph /\ ps ) -> ch )
3	2	3anidm12 1226	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:  ltnsym  7197  npncan2  7335  ltsubpos  7558  leaddle0  7581  subge02  7582  halfaddsub  8265  avglt1  8269