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Theorem nfcrd 2897
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 group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝐴(𝑥,𝑦)

Proof of Theorem nfcrd
StepHypRef Expression
1 nfcrd.1 . 2 (𝜑𝑥𝐴)
2 nfcr 2893 . 2 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2syl 17 1 (𝜑 → Ⅎ𝑥 𝑦𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnf 1780  wcel 2106  wnfc 2888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-nf 1781  df-clel 2814  df-nfc 2890
This theorem is referenced by:  nfeld  2915  dvelimdc  2928  nfraldw  3307  nfcsbd  3934  nfcsbw  3935  nfifd  4560  axextnd  10629  axrepndlem1  10630  axunndlem1  10633  axregnd  10642  axsepg2  35075  axsepg2ALT  35076  axextdist  35781  nfintd  48904  nfiund  48905  nfiundg  48906
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