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Theorem dfer2 6906
 Description: Alternate definition of equivalence predicate. (Contributed by NM, 3-Jan-1997.) (Revised by Mario Carneiro, 12-Aug-2015.)
Assertion
Ref Expression
dfer2
Distinct variable group:   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem dfer2
StepHypRef Expression
1 df-er 6905 . 2
2 cnvsym 5248 . . . . 5
3 cotr 5246 . . . . 5
42, 3anbi12i 679 . . . 4
5 unss 3521 . . . 4
6 19.28v 1918 . . . . . . . 8
76albii 1575 . . . . . . 7
8 19.26 1603 . . . . . . 7
97, 8bitri 241 . . . . . 6
109albii 1575 . . . . 5
11 19.26 1603 . . . . 5
1210, 11bitr2i 242 . . . 4
134, 5, 123bitr3i 267 . . 3
14133anbi3i 1146 . 2
151, 14bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wal 1549   wceq 1652   cun 3318   wss 3320   class class class wbr 4212  ccnv 4877   cdm 4878   ccom 4882   wrel 4883   wer 6902 This theorem is referenced by:  iserd  6931  trer  26319  riscer  26604  prter1  26728 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 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-er 6905
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