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Theorem nfceqi 2568
 Description: Equality theorem for class not-free. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfceqi.1
Assertion
Ref Expression
nfceqi

Proof of Theorem nfceqi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfceqi.1 . . . . 5
21eleq2i 2500 . . . 4
32nfbii 1578 . . 3
43albii 1575 . 2
5 df-nfc 2561 . 2
6 df-nfc 2561 . 2
74, 5, 63bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1549  wnf 1553   wceq 1652   wcel 1725  wnfc 2559 This theorem is referenced by:  nfcxfr  2569  nfcxfrd  2570 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-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-cleq 2429  df-clel 2432  df-nfc 2561
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