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  7756  prarloclemlo  7757  seq3f1oleml  10824  ccatswrd  11300  resqrexlemdecn  11635  pcdvdstr  12963  ennnfoneleminc  13095  prdssgrpd  13561  prdsmndd  13594  grprcan  13683  mulgnn0dir  13802  lmodprop2d  14427  lssintclm  14463  psrbaglesuppg  14751  restopnb  14975  cnptopresti  15032  blsscls2  15287