Theorem 3simpb 990

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 981	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )
2		3simpa 989	. 2 |- ( ( ph /\ ch /\ ps ) -> ( ph /\ ch ) )
3	1, 2	sylbi 120	1 |- ( ( ph /\ ps /\ ch ) -> ( ph /\ ch ) )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 973

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

This theorem depends on definitions:  df-bi 116  df-3an 975

This theorem is referenced by:  3adant2  1011  3adantl2  1149  3adantr2  1152  enq0tr  7396  ixxssixx  9859  rebtwn2zlemshrink  10210  zsumdc  11347  muldvds1  11778  dvds2add  11787  dvds2sub  11788  dvdstr  11790  pw2dvdslemn  12119  ctinf  12385  mndissubm  12697