Theorem simp-4l 531

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 523	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ph )
2	1	adantr 274	1 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  simp-5l  533  disjiun  3977  fnfi  6902  nninfisol  7097  sumeq2  11300  zsumdc  11325  modfsummod  11399  prodeq2  11498  zproddc  11520  cncnp  12870  fsumcncntop  13196  logbgcd1irrap  13528