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  7516  prarloclemlt  7756  prarloclemlo  7757  ccatswrd  11300  pfxccat3  11364  resqrexlemdecn  11635  summodclem2  12006  isumss2  12017  pcdvdstr  12963  ennnfoneleminc  13095  prdssgrpd  13561  prdsmndd  13594  grprcan  13683  mulgnn0dir  13802  mulgdir  13804  mulgass  13809  lmodprop2d  14427  lssintclm  14463  psrbaglesuppg  14751  restopnb  14975  blsscls2  15287