Theorem 3simpb 1022

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 1013	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )
2		3simpa 1021	. 2 |- ( ( ph /\ ch /\ ps ) -> ( ph /\ ch ) )
3	1, 2	sylbi 121	1 |- ( ( ph /\ ps /\ ch ) -> ( ph /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

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 1007

This theorem is referenced by:  3adant2  1043  3adantl2  1181  3adantr2  1184  enq0tr  7749  ixxssixx  10235  rebtwn2zlemshrink  10613  zsumdc  12070  muldvds1  12502  dvds2add  12511  dvds2sub  12512  dvdstr  12514  pw2dvdslemn  12862  ctinf  13181  mndissubm  13688  gsumfzconst  14058