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Theorem cleqf 2201
 Description: Establish equality between classes, using bound-variable hypotheses instead of distinct variable conditions. See also cleqh 2137. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
cleqf.1
cleqf.2
Assertion
Ref Expression
cleqf

Proof of Theorem cleqf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2034 . 2
2 nfv 1421 . . 3
3 cleqf.1 . . . . 5
43nfcri 2172 . . . 4
5 cleqf.2 . . . . 5
65nfcri 2172 . . . 4
74, 6nfbi 1481 . . 3
8 eleq1 2100 . . . 4
9 eleq1 2100 . . . 4
108, 9bibi12d 224 . . 3
112, 7, 10cbval 1637 . 2
121, 11bitr4i 176 1
 Colors of variables: wff set class Syntax hints:   wb 98  wal 1241   wceq 1243   wcel 1393  wnfc 2165 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-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167 This theorem is referenced by:  abid2f  2202  n0rf  3233  eq0  3239  iunab  3703  iinab  3718  sniota  4894
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