Theorem 3anidm13 1286

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 1199	. 2 |- ( ( ph /\ ph /\ ps ) -> ch )
3	2	3anidm12 1285	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

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

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  ltnsym  7980  npncan2  8121  ltsubpos  8348  leaddle0  8371  subge02  8372  halfaddsub  9087  avglt1  9091  pythagtriplem4  12196  pythagtriplem14  12205  rplogbid1  13465