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Theorem ercnv 6929
 Description: The converse of an equivalence relation is itself. (Contributed by Mario Carneiro, 12-Aug-2015.)
Assertion
Ref Expression
ercnv

Proof of Theorem ercnv
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 errel 6917 . 2
2 relcnv 5245 . . 3
3 id 21 . . . . . 6
43ersymb 6922 . . . . 5
5 vex 2961 . . . . . . 7
6 vex 2961 . . . . . . 7
75, 6brcnv 5058 . . . . . 6
8 df-br 4216 . . . . . 6
97, 8bitr3i 244 . . . . 5
10 df-br 4216 . . . . 5
114, 9, 103bitr3g 280 . . . 4
1211eqrelrdv2 4978 . . 3
132, 12mpanl1 663 . 2
141, 13mpancom 652 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  cop 3819   class class class wbr 4215  ccnv 4880   wrel 4886   wer 6905 This theorem is referenced by:  errn  6930 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-xp 4887  df-rel 4888  df-cnv 4889  df-er 6908
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