Theorem 3anidm13 1309

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 1212	. 2 |- ( ( ph /\ ph /\ ps ) -> ch )
3	2	3anidm12 1308	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  ltnsym  8193  npncan2  8334  ltsubpos  8562  leaddle0  8585  subge02  8586  halfaddsub  9306  avglt1  9311  pythagtriplem4  12706  pythagtriplem14  12715  rplogbid1  15534