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Theorem eqvincf 3064
 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 3063 . 2
3 eqvincf.1 . . . . 5
43nfeq2 2583 . . . 4
5 eqvincf.2 . . . . 5
65nfeq2 2583 . . . 4
74, 6nfan 1846 . . 3
8 nfv 1629 . . 3
9 eqeq1 2442 . . . 4
10 eqeq1 2442 . . . 4
119, 10anbi12d 692 . . 3
127, 8, 11cbvex 1983 . 2
132, 12bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  wnfc 2559  cvv 2956 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958
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