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Theorem releqi 4788
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 4787 . 2  |-  ( A  =  B  ->  ( Rel  A  <->  Rel  B ) )
31, 2ax-mp 8 1  |-  ( Rel 
A  <->  Rel  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1632   Rel wrel 4710
This theorem is referenced by:  reliun  4822  reluni  4824  relint  4825  reldmmpt2  5971  tfrlem6  6414  relsdom  6886  cda1dif  7818  0rest  13350  firest  13353  2oppchomf  13643  xpcbas  13968  oppchofcl  14050  oyoncl  14060  releqg  14680  reldvdsr  15442  eltopspOLD  16672  restbas  16905  hlimcaui  21832  relbigcup  24508  fnsingle  24529  funimage  24538  colinrel  24752
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179  df-rel 4712
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