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

Theorem nfnfc 2231
Description: Hypothesis builder for 𝑦𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfnfc.1 𝑥𝐴
Assertion
Ref Expression
nfnfc 𝑥𝑦𝐴

Proof of Theorem nfnfc
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2214 . 2 (𝑦𝐴 ↔ ∀𝑧𝑦 𝑧𝐴)
2 nfnfc.1 . . . . 5 𝑥𝐴
32nfcri 2219 . . . 4 𝑥 𝑧𝐴
43nfnf 1512 . . 3 𝑥𝑦 𝑧𝐴
54nfal 1511 . 2 𝑥𝑧𝑦 𝑧𝐴
61, 5nfxfr 1406 1 𝑥𝑦𝐴
Colors of variables: wff set class
Syntax hints:  wal 1285  wnf 1392  wcel 1436  wnfc 2212
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-cleq 2078  df-clel 2081  df-nfc 2214
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator