Theorem simplr3 1067

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simplr3	|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

Proof of Theorem simplr3

Step	Hyp	Ref	Expression
1		simpr3 1031	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

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:  netap  7473  prarloclemlt  7713  prarloclemlo  7714  ccatswrd  11255  pfxccat3  11319  resqrexlemdecn  11590  summodclem2  11961  isumss2  11972  pcdvdstr  12918  ennnfoneleminc  13050  prdssgrpd  13516  prdsmndd  13549  grprcan  13638  mulgnn0dir  13757  mulgdir  13759  mulgass  13764  lmodprop2d  14381  lssintclm  14417  psrbaglesuppg  14705  restopnb  14924  blsscls2  15236