Theorem simp312 1131

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 1014	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant3 1006	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 960

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 962

This theorem is referenced by:  dalemrot  32989  dalem-cly  33003  dath2  33069  cdleme26e  33691  cdleme38m  33795  cdleme38n  33796  cdleme39n  33798  cdlemg28b  34035  cdlemk7  34180  cdlemk11  34181  cdlemk12  34182  cdlemk7u  34202  cdlemk11u  34203  cdlemk12u  34204  cdlemk22  34225  cdlemk23-3  34234  cdlemk25-3  34236