Theorem simp31r 1185

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

Assertion

Ref	Expression
simp31r	|- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )

Proof of Theorem simp31r

Step	Hyp	Ref	Expression
1		simp1r 1086	. 2 |- ( ( ( ph /\ ps ) /\ ch /\ th ) -> ps )
2	1	3ad2ant3 1084	1 |- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  ps-2c  34814  cdlema1N  35077  cdlemednpq  35586  cdleme19e  35595  cdleme20h  35604  cdleme20j  35606  cdleme20l2  35609  cdleme20m  35611  cdleme22a  35628  cdleme22cN  35630  cdleme22f2  35635  cdleme26f2ALTN  35652  cdleme37m  35750  cdlemg12f  35936  cdlemg12g  35937  cdlemg12  35938  cdlemg28a  35981  cdlemg29  35993  cdlemg33a  35994  cdlemg36  36002  cdlemk16a  36144  cdlemk21-2N  36179  cdlemk54  36246  dihord10  36512