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Theorem 3simpb 937
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3simpb  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ph  /\  ch ) )

Proof of Theorem 3simpb
StepHypRef Expression
1 3ancomb 928 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )
2 3simpa 936 . 2  |-  ( (
ph  /\  ch  /\  ps )  ->  ( ph  /\  ch ) )
31, 2sylbi 119 1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ph  /\  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
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 922
This theorem is referenced by:  3adant2  958  3adantl2  1096  3adantr2  1099  enq0tr  6686  ixxssixx  9001  rebtwn2zlemshrink  9340  muldvds1  10365  dvds2add  10374  dvds2sub  10375  dvdstr  10377  pw2dvdslemn  10687
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