Theorem 3simpb 936

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 927	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )
2		3simpa 935	. 2 |- ( ( ph /\ ch /\ ps ) -> ( ph /\ ch ) )
3	1, 2	sylbi 119	1 |- ( ( ph /\ ps /\ ch ) -> ( ph /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  3adant2  957  3adantl2  1095  3adantr2  1098  enq0tr  6624  ixxssixx  8925  qbtwnzlemshrink  9258  rebtwn2zlemshrink  9262  muldvds1  10220  dvds2add  10229  dvds2sub  10230  dvdstr  10232  pw2dvdslemn  10543