Theorem simp311 1152

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 1035	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )
2	1	3ad2ant3 1028	1 |- ( ( et /\ ze /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 982

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 188  df-an 372  df-3an 984

This theorem is referenced by:  dalem-clpjq  33121  dath2  33221  cdleme26e  33845  cdleme38m  33949  cdleme38n  33950  cdleme39n  33952  cdlemg28b  34189  cdlemk7  34334  cdlemk11  34335  cdlemk12  34336  cdlemk7u  34356  cdlemk11u  34357  cdlemk12u  34358  cdlemk22  34379  cdlemk23-3  34388  cdlemk25-3  34390