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Theorem releqi 4534
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 4533 . 2  |-  ( A  =  B  ->  ( Rel  A  <->  Rel  B ) )
31, 2ax-mp 7 1  |-  ( Rel 
A  <->  Rel  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1290   Rel wrel 4457
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-in 3006  df-ss 3013  df-rel 4459
This theorem is referenced by:  reliun  4571  reluni  4573  relint  4574  reldmmpt2  5770  tfrlem6  6095
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