Theorem 3simpb 962

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 953	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )
2		3simpa 961	. 2 |- ( ( ph /\ ch /\ ps ) -> ( ph /\ ch ) )
3	1, 2	sylbi 120	1 |- ( ( ph /\ ps /\ ch ) -> ( ph /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 945

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

This theorem depends on definitions:  df-bi 116  df-3an 947

This theorem is referenced by:  3adant2  983  3adantl2  1121  3adantr2  1124  enq0tr  7190  ixxssixx  9578  rebtwn2zlemshrink  9924  zsumdc  11045  muldvds1  11366  dvds2add  11375  dvds2sub  11376  dvdstr  11378  pw2dvdslemn  11688  ctinf  11788