Theorem simp312 1154

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 1037	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant3 1029	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 983

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 189  df-an 373  df-3an 985

This theorem is referenced by:  dalemrot  33185  dalem-cly  33199  dath2  33265  cdleme26e  33889  cdleme38m  33993  cdleme38n  33994  cdleme39n  33996  cdlemg28b  34233  cdlemk7  34378  cdlemk11  34379  cdlemk12  34380  cdlemk7u  34400  cdlemk11u  34401  cdlemk12u  34402  cdlemk22  34423  cdlemk23-3  34432  cdlemk25-3  34434