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Theorem cleqf 2179
Description: Establish equality between classes, using bound-variable hypotheses instead of distinct variable conditions. See also cleqh 2115. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
cleqf.1  F/_
cleqf.2  F/_
Assertion
Ref Expression
cleqf

Proof of Theorem cleqf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2012 . 2
2 nfv 1398 . . 3  F/
3 cleqf.1 . . . . 5  F/_
43nfcri 2150 . . . 4  F/
5 cleqf.2 . . . . 5  F/_
65nfcri 2150 . . . 4  F/
74, 6nfbi 1459 . . 3  F/
8 eleq1 2078 . . . 4
9 eleq1 2078 . . . 4
108, 9bibi12d 224 . . 3
112, 7, 10cbval 1615 . 2
121, 11bitr4i 176 1
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1224   wceq 1226   wcel 1370   F/_wnfc 2143
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 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-cleq 2011  df-clel 2014  df-nfc 2145
This theorem is referenced by:  abid2f  2180  n0rf  3206  eq0  3212  iunab  3673  iinab  3688  sniota  4817
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