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Theorem nfcrd 2972
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfcrd.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 nfcrd.1 . 2 (𝜑𝑥𝐴)
2 nfcr 2969 . 2 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2syl 17 1 (𝜑 → Ⅎ𝑥 𝑦𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnf 1783  wcel 2113  wnfc 2964
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-12 2176
This theorem depends on definitions:  df-bi 209  df-ex 1780  df-nfc 2966
This theorem is referenced by:  nfeqd  2991  nfeld  2992  dvelimdc  3008  nfcsbd  3911  nfcsbw  3912  nfifd  4498  axextnd  10016  axrepndlem1  10017  axunndlem1  10020  axregnd  10029  axextdist  33048  wl-clelsb3df  34867  nfintd  44783  nfiund  44784  nfiundg  44785
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