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Theorem eqvincf 3194
 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 3193 . 2
3 eqvincf.1 . . . . 5
43nfeq2 2633 . . . 4
5 eqvincf.2 . . . . 5
65nfeq2 2633 . . . 4
74, 6nfan 1866 . . 3
8 nfv 1674 . . 3
9 eqeq1 2458 . . . 4
10 eqeq1 2458 . . . 4
119, 10anbi12d 710 . . 3
127, 8, 11cbvex 1982 . 2
132, 12bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1370  wex 1587   wcel 1758  wnfc 2602  cvv 3078 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3080 This theorem is referenced by: (None)
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