ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3simpb Unicode version

Theorem 3simpb 939
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 930 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )
2 3simpa 938 . 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 922
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 924
This theorem is referenced by:  3adant2  960  3adantl2  1098  3adantr2  1101  enq0tr  6930  ixxssixx  9245  rebtwn2zlemshrink  9586  zisum  10656  muldvds1  10688  dvds2add  10697  dvds2sub  10698  dvdstr  10700  pw2dvdslemn  11010
  Copyright terms: Public domain W3C validator