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Theorem eqvincf 2669
 Description: A variable introduction law for class equality, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 14-Sep-2003.)
Hypotheses
Ref Expression
eqvincf.1
eqvincf.2
eqvincf.3
Assertion
Ref Expression
eqvincf

Proof of Theorem eqvincf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqvincf.3 . . 3
21eqvinc 2667 . 2
3 eqvincf.1 . . . . 5
43nfeq2 2189 . . . 4
5 eqvincf.2 . . . . 5
65nfeq2 2189 . . . 4
74, 6nfan 1457 . . 3
8 nfv 1421 . . 3
9 eqeq1 2046 . . . 4
10 eqeq1 2046 . . . 4
119, 10anbi12d 442 . . 3
127, 8, 11cbvex 1639 . 2
132, 12bitri 173 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wceq 1243  wex 1381   wcel 1393  wnfc 2165  cvv 2557 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-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559 This theorem is referenced by: (None)
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