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  11456  pfxccat3  11520  resqrexlemdecn  11792  summodclem2  12165  isumss2  12176  pcdvdstr  13126  ennnfoneleminc  13351  grprcan  13891  mulgnn0dir  14004  mulgdir  14006  mulgass  14011  prdssgrpd  14240  prdsmndd  14243  lmodprop2d  14734  lssintclm  14770  psrbaglesuppg  15106  restopnb  15331  blsscls2  15643