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Theorem nfcd 2569
 Description: Deduce that a class does not have free in it. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfcd.1
nfcd.2
Assertion
Ref Expression
nfcd
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem nfcd
StepHypRef Expression
1 nfcd.1 . . 3
2 nfcd.2 . . 3
31, 2alrimi 1782 . 2
4 df-nfc 2563 . 2
53, 4sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1550  wnf 1554   wcel 1726  wnfc 2561 This theorem is referenced by:  nfabd2  2592  dvelimdc  2594  sbnfc2  3311  riotasv2dOLD  6597 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555  df-nfc 2563
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