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Theorem nfcr 2167
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfcr (xA → Ⅎx y A)
Distinct variable groups:   x,y   y,A
Allowed substitution hint:   A(x)

Proof of Theorem nfcr
StepHypRef Expression
1 df-nfc 2164 . 2 (xAyx y A)
2 sp 1398 . 2 (yx y A → Ⅎx y A)
31, 2sylbi 114 1 (xA → Ⅎx y A)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  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-4 1397
This theorem depends on definitions:  df-bi 110  df-nfc 2164
This theorem is referenced by:  nfcrii  2168  nfcrd  2188  abidnf  2703  csbtt  2856  csbnestgf  2892
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