Theorem simplr3 1072

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 1036	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ch )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  netap  7620  prarloclemlt  7860  prarloclemlo  7861  ccatswrd  11442  pfxccat3  11506  resqrexlemdecn  11778  summodclem2  12149  isumss2  12160  pcdvdstr  13106  ennnfoneleminc  13302  grprcan  13842  mulgnn0dir  13955  mulgdir  13957  mulgass  13962  prdssgrpd  14191  prdsmndd  14194  lmodprop2d  14685  lssintclm  14721  psrbaglesuppg  15057  restopnb  15282  blsscls2  15594