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 )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  prarloclemlt  7860  prarloclemlo  7861  seq3f1oleml  10966  ccatswrd  11456  resqrexlemdecn  11792  pcdvdstr  13126  ennnfoneleminc  13351  grprcan  13891  mulgnn0dir  14004  prdssgrpd  14240  prdsmndd  14243  lmodprop2d  14734  lssintclm  14770  psrbaglesuppg  15106  restopnb  15331  cnptopresti  15388  blsscls2  15643