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Theorem 3simpb 964
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 955 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )
2 3simpa 963 . 2  |-  ( (
ph  /\  ch  /\  ps )  ->  ( ph  /\  ch ) )
31, 2sylbi 120 1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ph  /\  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
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 949
This theorem is referenced by:  3adant2  985  3adantl2  1123  3adantr2  1126  enq0tr  7210  ixxssixx  9653  rebtwn2zlemshrink  9999  zsumdc  11121  muldvds1  11445  dvds2add  11454  dvds2sub  11455  dvdstr  11457  pw2dvdslemn  11770  ctinf  11870
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