Theorem simp-4l 541

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
simp-4l	|- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ph )

Proof of Theorem simp-4l

Step	Hyp	Ref	Expression
1		simplll 533	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ph )
2	1	adantr 276	1 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ wa 104

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 is referenced by:  simp-5l  543  disjiun  4029  fnfi  7011  nninfisol  7208  sumeq2  11541  zsumdc  11566  modfsummod  11640  prodeq2  11739  zproddc  11761  mulgval  13328  cncnp  14550  fsumcncntop  14887  dvmptfsum  15045  dvply2g  15086  logbgcd1irrap  15290