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  7621  prarloclemlt  7861  prarloclemlo  7862  ccatswrd  11458  summodclem2  12168  pcdvdstr  13129  grprcan  13895  prdssgrpd  14275  prdsmndd  14278  lmodprop2d  14769  lssintclm  14805  psrbaglesuppg  15141  restopnb  15373  blsscls2  15685