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  4024  fnfi  6995  nninfisol  7192  sumeq2  11502  zsumdc  11527  modfsummod  11601  prodeq2  11700  zproddc  11722  mulgval  13192  cncnp  14398  fsumcncntop  14724  logbgcd1irrap  15102