Theorem simp311 1135

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 1018	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )
2	1	3ad2ant3 1011	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

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:  dalem-clpjq  33286  dath2  33386  cdleme26e  34008  cdleme38m  34112  cdleme38n  34113  cdleme39n  34115  cdlemg28b  34352  cdlemk7  34497  cdlemk11  34498  cdlemk12  34499  cdlemk7u  34519  cdlemk11u  34520  cdlemk12u  34521  cdlemk22  34542  cdlemk23-3  34551  cdlemk25-3  34553