Theorem 3simpb 1021

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

Ref	Expression
3simpb	|- ( ( ph /\ ps /\ ch ) -> ( ph /\ ch ) )

Proof of Theorem 3simpb

Step	Hyp	Ref	Expression
1		3ancomb 1012	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )
2		3simpa 1020	. 2 |- ( ( ph /\ ch /\ ps ) -> ( ph /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ph /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  3adant2  1042  3adantl2  1180  3adantr2  1183  enq0tr  7654  ixxssixx  10137  rebtwn2zlemshrink  10514  zsumdc  11947  muldvds1  12379  dvds2add  12388  dvds2sub  12389  dvdstr  12391  pw2dvdslemn  12739  ctinf  13053  mndissubm  13560  gsumfzconst  13930