Theorem simplr3 1068

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 1032	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  netap  7568  prarloclemlt  7808  prarloclemlo  7809  ccatswrd  11362  pfxccat3  11426  resqrexlemdecn  11697  summodclem2  12068  isumss2  12079  pcdvdstr  13025  ennnfoneleminc  13162  prdssgrpd  13628  prdsmndd  13661  grprcan  13750  mulgnn0dir  13869  mulgdir  13871  mulgass  13876  lmodprop2d  14496  lssintclm  14532  psrbaglesuppg  14821  restopnb  15046  blsscls2  15358