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Theorem cleqf 2598
 Description: Establish equality between classes, using bound-variable hypotheses instead of distinct variable conditions. (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 2432 . 2
2 nfv 1630 . . 3
3 cleqf.1 . . . . 5
43nfcri 2568 . . . 4
5 cleqf.2 . . . . 5
65nfcri 2568 . . . 4
74, 6nfbi 1857 . . 3
8 eleq1 2498 . . . 4
9 eleq1 2498 . . . 4
108, 9bibi12d 314 . . 3
112, 7, 10cbval 1983 . 2
121, 11bitr4i 245 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1550   wceq 1653   wcel 1726  wnfc 2561 This theorem is referenced by:  abid2f  2599  n0f  3638  iunab  4139  iinab  4154  sniota  5447  mbfposr  19546  mbfinf  19559  itg1climres  19608  compab  27622  rfcnpre1  27668  rfcnpre2  27680  bnj1366  29263 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2431  df-clel 2434  df-nfc 2563
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