Theorem simp312 1157

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 1040	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant3 1032	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 986

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 988

This theorem is referenced by:  dalemrot  33234  dalem-cly  33248  dath2  33314  cdleme26e  33938  cdleme38m  34042  cdleme38n  34043  cdleme39n  34045  cdlemg28b  34282  cdlemk7  34427  cdlemk11  34428  cdlemk12  34429  cdlemk7u  34449  cdlemk11u  34450  cdlemk12u  34451  cdlemk22  34472  cdlemk23-3  34481  cdlemk25-3  34483