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Theorem cleqf 2513
 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 2347 . 2
2 nfv 1619 . . 3
3 cleqf.1 . . . . 5
43nfcri 2483 . . . 4
5 cleqf.2 . . . . 5
65nfcri 2483 . . . 4
74, 6nfbi 1834 . . 3
8 eleq1 2413 . . . 4
9 eleq1 2413 . . . 4
108, 9bibi12d 312 . . 3
112, 7, 10cbval 1984 . 2
121, 11bitr4i 243 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540   wceq 1642   wcel 1710  wnfc 2476 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478 This theorem is referenced by:  abid2f  2514  n0f  3558  iunab  4012  iinab  4027  sniota  4369
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