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Theorem eqbrriv 4494
 Description: Inference from extensionality principle for relations. (Contributed by NM, 12-Dec-2006.)
Hypotheses
Ref Expression
eqbrriv.1
eqbrriv.2
eqbrriv.3
Assertion
Ref Expression
eqbrriv
Distinct variable groups:   ,,   ,,

Proof of Theorem eqbrriv
StepHypRef Expression
1 eqbrriv.1 . 2
2 eqbrriv.2 . 2
3 eqbrriv.3 . . 3
4 df-br 3815 . . 3
5 df-br 3815 . . 3
63, 4, 53bitr3i 208 . 2
71, 2, 6eqrelriiv 4493 1
 Colors of variables: wff set class Syntax hints:   wb 103   wceq 1287   wcel 1436  cop 3428   class class class wbr 3814   wrel 4409 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-14 1448  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-sep 3925  ax-pow 3977  ax-pr 4003 This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-un 2990  df-in 2992  df-ss 2999  df-pw 3411  df-sn 3431  df-pr 3432  df-op 3434  df-br 3815  df-opab 3869  df-xp 4410  df-rel 4411 This theorem is referenced by:  resco  4892  tpostpos  5964
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