ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfcrd GIF version

Theorem nfcrd 2296
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 2274 . 2 (𝑥𝐴 → Ⅎ𝑥 𝑦𝐴)
31, 2syl 14 1 (𝜑 → Ⅎ𝑥 𝑦𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1437  wcel 1481  wnfc 2269
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1488
This theorem depends on definitions:  df-bi 116  df-nfc 2271
This theorem is referenced by:  nfeqd  2297  nfeld  2298  dvelimdc  2302  nfcsbd  3037  nfifd  3500
  Copyright terms: Public domain W3C validator