Theorem simp312 1136

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 1019	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant3 1011	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 965

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 967

This theorem is referenced by:  dalemrot  33301  dalem-cly  33315  dath2  33381  cdleme26e  34003  cdleme38m  34107  cdleme38n  34108  cdleme39n  34110  cdlemg28b  34347  cdlemk7  34492  cdlemk11  34493  cdlemk12  34494  cdlemk7u  34514  cdlemk11u  34515  cdlemk12u  34516  cdlemk22  34537  cdlemk23-3  34546  cdlemk25-3  34548