Theorem 3anidm13 1337

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 1240	. 2 |- ( ( ph /\ ph /\ ps ) -> ch )
3	2	3anidm12 1336	1 |- ( ( ph /\ ps ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  ltnsym  8411  npncan2  8554  ltsubpos  8783  leaddle0  8806  subge02  8807  halfaddsub  9543  avglt1  9548  bcm1n  11221  pythagtriplem4  13067  pythagtriplem14  13076  rplogbid1  16102