Theorem simplr2 1066

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 1030	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 1006

This theorem is referenced by:  prarloclemlt  7713  prarloclemlo  7714  seq3f1oleml  10778  ccatswrd  11251  resqrexlemdecn  11573  pcdvdstr  12901  ennnfoneleminc  13033  prdssgrpd  13499  prdsmndd  13532  grprcan  13621  mulgnn0dir  13740  lmodprop2d  14364  lssintclm  14400  psrbaglesuppg  14688  restopnb  14907  cnptopresti  14964  blsscls2  15219