Theorem simp312 1209

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 1092	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant3 1084	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  dalemrot  34943  dalem-cly  34957  dath2  35023  cdleme26e  35647  cdleme38m  35751  cdleme38n  35752  cdleme39n  35754  cdlemg28b  35991  cdlemk7  36136  cdlemk11  36137  cdlemk12  36138  cdlemk7u  36158  cdlemk11u  36159  cdlemk12u  36160  cdlemk22  36181  cdlemk23-3  36190  cdlemk25-3  36192