Theorem simp-4l 543

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 535	. 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  545  disjiun  4103  fnfi  7202  mapfi  7213  nninfisol  7423  swrdccatin1  11413  sumeq2  12040  zsumdc  12066  modfsummod  12140  prodeq2  12239  zproddc  12261  mulgval  13831  mplsubgfilemcl  14846  cncnp  15087  fsumcncntop  15424  dvmptfsum  15582  dvply2g  15623  logbgcd1irrap  15827  upgriswlkdc  16347  clwwlkccatlem  16387