Theorem simplr1 1070

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simplr1	|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ph )

Proof of Theorem simplr1

Step	Hyp	Ref	Expression
1		simpr1 1034	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ph )
2	1	adantr 276	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ph )

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  7626  prarloclemlt  7866  prarloclemlo  7867  ccatswrd  11463  summodclem2  12173  pcdvdstr  13134  grprcan  13900  prdssgrpd  14297  prdsmndd  14300  lmodprop2d  14793  lssintclm  14829  psrbaglesuppg  15170  mplsubgfilemcl  15232  restopnb  15424  blsscls2  15736