Theorem simplr2 1071

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 1035	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1009

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 1011

This theorem is referenced by:  prarloclemlt  7850  prarloclemlo  7851  seq3f1oleml  10931  ccatswrd  11420  resqrexlemdecn  11756  pcdvdstr  13084  ennnfoneleminc  13280  grprcan  13819  mulgnn0dir  13932  prdssgrpd  14168  prdsmndd  14171  lmodprop2d  14657  lssintclm  14693  psrbaglesuppg  14980  restopnb  15205  cnptopresti  15262  blsscls2  15517