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Theorem nfcrd 2800
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 𝑦𝐴)
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 2785 . 2 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2syl 17 1 (𝜑 → Ⅎ𝑥 𝑦𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnf 1748  wcel 2030  wnfc 2780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745  df-nfc 2782
This theorem is referenced by:  nfeqd  2801  nfeld  2802  dvelimdc  2815  nfcsbd  3583  nfifd  4147  axextnd  9451  axrepndlem1  9452  axunndlem1  9455  axregnd  9464  axextdist  31829  nfintd  42745  nfiund  42746
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