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Theorem nfci 2618
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  |-  F/ x  y  e.  A
Assertion
Ref Expression
nfci  |-  F/_ x A
Distinct variable groups:    x, y    y, A
Allowed substitution hint:    A( x)

Proof of Theorem nfci
StepHypRef Expression
1 df-nfc 2617 . 2  |-  ( F/_ x A  <->  A. y F/ x  y  e.  A )
2 nfci.1 . 2  |-  F/ x  y  e.  A
31, 2mpgbir 1605 1  |-  F/_ x A
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1599    e. wcel 1767   F/_wnfc 2615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601
This theorem depends on definitions:  df-bi 185  df-nfc 2617
This theorem is referenced by:  nfcii  2619  nfcv  2629  nfab1  2631  nfab  2633  fpwrelmap  27379  esumfzf  27900  climsuse  31473  climinff  31476  bj-nfab1  33853
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