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Theorem releqd 4693
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 4691 . 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 104    = wceq 1348   Rel wrel 4614
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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-in 3127  df-ss 3134  df-rel 4616
This theorem is referenced by:  dftpos3  6239  tposfo2  6244  tposf12  6246  lmreltop  12952  cnprcl2k  12965
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