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Theorem releqd 4450
Description: Equality deduction for the relation predicate. (Contributed by NM, 8-Mar-2014.)
Hypothesis
Ref Expression
releqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
releqd  |-  ( ph  ->  ( Rel  A  <->  Rel  B ) )

Proof of Theorem releqd
StepHypRef Expression
1 releqd.1 . 2  |-  ( ph  ->  A  =  B )
2 releq 4448 . 2  |-  ( A  =  B  ->  ( Rel  A  <->  Rel  B ) )
31, 2syl 14 1  |-  ( ph  ->  ( Rel  A  <->  Rel  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    = wceq 1285   Rel wrel 4376
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987  df-rel 4378
This theorem is referenced by:  dftpos3  5911  tposfo2  5916  tposf12  5918
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