Theorem simplr3 1065

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 1029	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

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:  netap  7451  prarloclemlt  7691  prarloclemlo  7692  ccatswrd  11217  pfxccat3  11281  resqrexlemdecn  11538  summodclem2  11908  isumss2  11919  pcdvdstr  12865  ennnfoneleminc  12997  prdssgrpd  13463  prdsmndd  13496  grprcan  13585  mulgnn0dir  13704  mulgdir  13706  mulgass  13711  lmodprop2d  14327  lssintclm  14363  psrbaglesuppg  14651  restopnb  14870  blsscls2  15182