Theorem simp311 1155

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp311	|- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

Proof of Theorem simp311

Step	Hyp	Ref	Expression
1		simp11 1038	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )
2	1	3ad2ant3 1031	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 985

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 987

This theorem is referenced by:  dalem-clpjq  33202  dath2  33302  cdleme26e  33926  cdleme38m  34030  cdleme38n  34031  cdleme39n  34033  cdlemg28b  34270  cdlemk7  34415  cdlemk11  34416  cdlemk12  34417  cdlemk7u  34437  cdlemk11u  34438  cdlemk12u  34439  cdlemk22  34460  cdlemk23-3  34469  cdlemk25-3  34471