Theorem simp312 1145

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 1028	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant3 1020	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 974

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 369  df-3an 976

This theorem is referenced by:  dalemrot  32655  dalem-cly  32669  dath2  32735  cdleme26e  33359  cdleme38m  33463  cdleme38n  33464  cdleme39n  33466  cdlemg28b  33703  cdlemk7  33848  cdlemk11  33849  cdlemk12  33850  cdlemk7u  33870  cdlemk11u  33871  cdlemk12u  33872  cdlemk22  33893  cdlemk23-3  33902  cdlemk25-3  33904