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Theorem eqvincf 2967
 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 2966 . 2
3 eqvincf.1 . . . . 5
43nfeq2 2500 . . . 4
5 eqvincf.2 . . . . 5
65nfeq2 2500 . . . 4
74, 6nfan 1824 . . 3
8 nfv 1619 . . 3
9 eqeq1 2359 . . . 4
10 eqeq1 2359 . . . 4
119, 10anbi12d 691 . . 3
127, 8, 11cbvex 1985 . 2
132, 12bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  wnfc 2476  cvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by: (None)
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