Theorem simplr2 1064

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 1028	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

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 1004

This theorem is referenced by:  prarloclemlt  7691  prarloclemlo  7692  seq3f1oleml  10750  ccatswrd  11217  resqrexlemdecn  11538  pcdvdstr  12865  ennnfoneleminc  12997  prdssgrpd  13463  prdsmndd  13496  grprcan  13585  mulgnn0dir  13704  lmodprop2d  14327  lssintclm  14363  psrbaglesuppg  14651  restopnb  14870  cnptopresti  14927  blsscls2  15182