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Theorem releqd 4964
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 4962 . 2  |-  ( A  =  B  ->  ( Rel  A  <->  Rel  B ) )
31, 2syl 16 1  |-  ( ph  ->  ( Rel  A  <->  Rel  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    = wceq 1653   Rel wrel 4886
This theorem is referenced by:  dftpos3  6500  tposfo2  6505  tposf12  6507  imasaddfnlem  13758  imasvscafn  13767  cnextrel  18099  relfae  24603  dibvalrel  32035  dicvalrelN  32057  diclspsn  32066  dihvalrel  32151  dih1  32158  dihmeetlem4preN  32178
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-in 3329  df-ss 3336  df-rel 4888
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