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  7463  prarloclemlt  7703  prarloclemlo  7704  ccatswrd  11241  pfxccat3  11305  resqrexlemdecn  11563  summodclem2  11933  isumss2  11944  pcdvdstr  12890  ennnfoneleminc  13022  prdssgrpd  13488  prdsmndd  13521  grprcan  13610  mulgnn0dir  13729  mulgdir  13731  mulgass  13736  lmodprop2d  14352  lssintclm  14388  psrbaglesuppg  14676  restopnb  14895  blsscls2  15207