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Theorem eqbrrdv 4965
 Description: Deduction from extensionality principle for relations. (Contributed by Mario Carneiro, 3-Jan-2017.)
Hypotheses
Ref Expression
eqbrrdv.1
eqbrrdv.2
eqbrrdv.3
Assertion
Ref Expression
eqbrrdv
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem eqbrrdv
StepHypRef Expression
1 eqbrrdv.3 . . . 4
2 df-br 4205 . . . 4
3 df-br 4205 . . . 4
41, 2, 33bitr3g 279 . . 3
54alrimivv 1642 . 2
6 eqbrrdv.1 . . 3
7 eqbrrdv.2 . . 3
8 eqrel 4957 . . 3
96, 7, 8syl2anc 643 . 2
105, 9mpbird 224 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652   wcel 1725  cop 3809   class class class wbr 4204   wrel 4875 This theorem is referenced by:  eqbrrdva  5034  oppcsect2  13992 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-xp 4876  df-rel 4877
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