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Theorem releqi 4590
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 4589 . 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 1314   Rel wrel 4512
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 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-in 3045  df-ss 3052  df-rel 4514
This theorem is referenced by:  reliun  4628  reluni  4630  relint  4631  reldmmpo  5848  tfrlem6  6179  psmetrel  12386  metrel  12406  xmetrel  12407  xmetf  12414  mopnrel  12505
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