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

Theorem nfcxfrd 2251
Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfceqi.1 𝐴 = 𝐵
nfcxfrd.2 (𝜑𝑥𝐵)
Assertion
Ref Expression
nfcxfrd (𝜑𝑥𝐴)

Proof of Theorem nfcxfrd
StepHypRef Expression
1 nfcxfrd.2 . 2 (𝜑𝑥𝐵)
2 nfceqi.1 . . 3 𝐴 = 𝐵
32nfceqi 2249 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 133 1 (𝜑𝑥𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1312  wnfc 2240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1404  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-4 1468  ax-17 1487  ax-ial 1495  ax-ext 2095
This theorem depends on definitions:  df-bi 116  df-nf 1418  df-cleq 2106  df-clel 2109  df-nfc 2242
This theorem is referenced by:  nfcsb1d  2997  nfcsbd  3000  nfifd  3463  nfunid  3707  nfiotadxy  5047  nfriotadxy  5690  nfovd  5752  nfnegd  7875
  Copyright terms: Public domain W3C validator