Theorem simp312 1144

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp312	|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Proof of Theorem simp312

Step	Hyp	Ref	Expression
1		simp12 1027	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant3 1019	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975

This theorem is referenced by:  dalemrot  34453  dalem-cly  34467  dath2  34533  cdleme26e  35155  cdleme38m  35259  cdleme38n  35260  cdleme39n  35262  cdlemg28b  35499  cdlemk7  35644  cdlemk11  35645  cdlemk12  35646  cdlemk7u  35666  cdlemk11u  35667  cdlemk12u  35668  cdlemk22  35689  cdlemk23-3  35698  cdlemk25-3  35700