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Theorem eqbrrdv 4437
 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 3765 . . . 4
3 df-br 3765 . . . 4
41, 2, 33bitr3g 211 . . 3
54alrimivv 1755 . 2
6 eqbrrdv.1 . . 3
7 eqbrrdv.2 . . 3
8 eqrel 4429 . . 3
96, 7, 8syl2anc 391 . 2
105, 9mpbird 156 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243   wcel 1393  cop 3378   class class class wbr 3764   wrel 4350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-xp 4351  df-rel 4352 This theorem is referenced by:  eqbrrdva  4505
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