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Theorem nfci 2165
Description: Deduce that a class A does not have x free in it. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfci.1 x y A
Assertion
Ref Expression
nfci xA
Distinct variable groups:   x,y   y,A
Allowed substitution hint:   A(x)

Proof of Theorem nfci
StepHypRef Expression
1 df-nfc 2164 . 2 (xAyx y A)
2 nfci.1 . 2 x y A
31, 2mpgbir 1339 1 xA
Colors of variables: wff set class
Syntax hints:  wnf 1346   wcel 1390  wnfc 2162
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1335
This theorem depends on definitions:  df-bi 110  df-nfc 2164
This theorem is referenced by:  nfcii  2166  nfcv  2175  nfab1  2177  nfab  2179
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