Theorem simp311 1144

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 1027	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )
2	1	3ad2ant3 1020	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 974

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 369  df-3an 976

This theorem is referenced by:  dalem-clpjq  32634  dath2  32734  cdleme26e  33358  cdleme38m  33462  cdleme38n  33463  cdleme39n  33465  cdlemg28b  33702  cdlemk7  33847  cdlemk11  33848  cdlemk12  33849  cdlemk7u  33869  cdlemk11u  33870  cdlemk12u  33871  cdlemk22  33892  cdlemk23-3  33901  cdlemk25-3  33903