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Theorem nfceqi 2216
 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 2146 . . . 4
32nfbii 1403 . . 3
43albii 1400 . 2
5 df-nfc 2209 . 2
6 df-nfc 2209 . 2
74, 5, 63bitr4i 210 1
 Colors of variables: wff set class Syntax hints:   wb 103  wal 1283   wceq 1285  wnf 1390   wcel 1434  wnfc 2207 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-cleq 2075  df-clel 2078  df-nfc 2209 This theorem is referenced by:  nfcxfr  2217  nfcxfrd  2218
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