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Theorem refrel 19987
 Description: Refinement is a relation. (Contributed by Jeff Hankins, 18-Jan-2010.) (Revised by Thierry Arnoux, 3-Feb-2020.)
Assertion
Ref Expression
refrel

Proof of Theorem refrel
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ref 19984 . 2
21relopabi 5118 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   wceq 1383  wral 2793  wrex 2794   wss 3461  cuni 4234   wrel 4994  cref 19981 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-opab 4496  df-xp 4995  df-rel 4996  df-ref 19984 This theorem is referenced by:  isref  19988  refbas  19989  refssex  19990  reftr  19993  refun0  19994  locfinref  27822  refssfne  30152
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