Theorem simp311 1177

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 1060	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )
2	1	3ad2ant3 1053	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 1007

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 190  df-an 378  df-3an 1009

This theorem is referenced by:  dalem-clpjq  33273  dath2  33373  cdleme26e  33997  cdleme38m  34101  cdleme38n  34102  cdleme39n  34104  cdlemg28b  34341  cdlemk7  34486  cdlemk11  34487  cdlemk12  34488  cdlemk7u  34508  cdlemk11u  34509  cdlemk12u  34510  cdlemk22  34531  cdlemk23-3  34540  cdlemk25-3  34542