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Theorem nfci 2479
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 2478 . 2 (xAyx y A)
2 nfci.1 . 2 x y A
31, 2mpgbir 1550 1 xA
Colors of variables: wff setvar class
Syntax hints:  wnf 1544   wcel 1710  wnfc 2476
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546
This theorem depends on definitions:  df-bi 177  df-nfc 2478
This theorem is referenced by:  nfcii  2480  nfcv  2489  nfab1  2491  nfab  2493
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