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Theorem nfcrd 2188
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfeqd.1 (φxA)
Assertion
Ref Expression
nfcrd (φ → Ⅎx y A)
Distinct variable groups:   x,y   y,A
Allowed substitution hints:   φ(x,y)   A(x)

Proof of Theorem nfcrd
StepHypRef Expression
1 nfeqd.1 . 2 (φxA)
2 nfcr 2167 . 2 (xA → Ⅎx y A)
31, 2syl 14 1 (φ → Ⅎx y A)
Colors of variables: wff set class
Syntax hints:  wi 4  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:  nfeqd  2189  nfeld  2190  dvelimdc  2194  nfcsbd  2877  nfifd  3349
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