Theorem simplr2 1067

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

Assertion

Ref	Expression
simplr2	|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Proof of Theorem simplr2

Step	Hyp	Ref	Expression
1		simpr2 1031	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1007

This theorem is referenced by:  prarloclemlt  7808  prarloclemlo  7809  seq3f1oleml  10878  ccatswrd  11362  resqrexlemdecn  11697  pcdvdstr  13025  ennnfoneleminc  13162  prdssgrpd  13628  prdsmndd  13661  grprcan  13750  mulgnn0dir  13869  lmodprop2d  14496  lssintclm  14532  psrbaglesuppg  14821  restopnb  15046  cnptopresti  15103  blsscls2  15358