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Theorem nfcrd 2767
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 2753 . 2 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2syl 17 1 (𝜑 → Ⅎ𝑥 𝑦𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnf 1705  wcel 1987  wnfc 2748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-ex 1702  df-nfc 2750
This theorem is referenced by:  nfeqd  2768  nfeld  2769  dvelimdc  2782  nfcsbd  3531  nfifd  4086  axextnd  9357  axrepndlem1  9358  axunndlem1  9361  axregnd  9370  axextdist  31403  nfintd  41709  nfiund  41710
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