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Theorem releqd 4773
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 4771 . 2  |-  ( A  =  B  ->  ( Rel  A  <->  Rel  B ) )
31, 2syl 15 1  |-  ( ph  ->  ( Rel  A  <->  Rel  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1623   Rel wrel 4694
This theorem is referenced by:  dftpos3  6252  tposfo2  6257  tposf12  6259  imasaddfnlem  13430  imasvscafn  13439  cur1val  25198  bosser  26167  dibvalrel  31353  dicvalrelN  31375  diclspsn  31384  dihvalrel  31469  dih1  31476  dihmeetlem4preN  31496
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-in 3159  df-ss 3166  df-rel 4696
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