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Theorem nfcii 2247
Description: Deduce that a class  A does not have  x free in it. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfcii.1  |-  ( y  e.  A  ->  A. x  y  e.  A )
Assertion
Ref Expression
nfcii  |-  F/_ x A
Distinct variable groups:    x, y    y, A
Allowed substitution hint:    A( x)

Proof of Theorem nfcii
StepHypRef Expression
1 nfcii.1 . . 3  |-  ( y  e.  A  ->  A. x  y  e.  A )
21nfi 1421 . 2  |-  F/ x  y  e.  A
32nfci 2246 1  |-  F/_ x A
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312    e. wcel 1463   F/_wnfc 2243
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1408
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-nfc 2245
This theorem is referenced by: (None)
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