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

Theorem releqi 4684
Description: Equality inference for the relation predicate. (Contributed by NM, 8-Dec-2006.)
Hypothesis
Ref Expression
releqi.1  |-  A  =  B
Assertion
Ref Expression
releqi  |-  ( Rel 
A  <->  Rel  B )

Proof of Theorem releqi
StepHypRef Expression
1 releqi.1 . 2  |-  A  =  B
2 releq 4683 . 2  |-  ( A  =  B  ->  ( Rel  A  <->  Rel  B ) )
31, 2ax-mp 5 1  |-  ( Rel 
A  <->  Rel  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1342   Rel wrel 4606
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-11 1493  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-in 3120  df-ss 3127  df-rel 4608
This theorem is referenced by:  reliun  4722  reluni  4724  relint  4725  reldmmpo  5947  tfrlem6  6278  psmetrel  12920  metrel  12940  xmetrel  12941  xmetf  12948  mopnrel  13039
  Copyright terms: Public domain W3C validator