ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfreu1 GIF version

Theorem nfreu1 2538
Description: 𝑥 is not free in ∃!𝑥𝐴𝜑. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
nfreu1 𝑥∃!𝑥𝐴 𝜑

Proof of Theorem nfreu1
StepHypRef Expression
1 df-reu 2366 . 2 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥(𝑥𝐴𝜑))
2 nfeu1 1959 . 2 𝑥∃!𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1408 1 𝑥∃!𝑥𝐴 𝜑
Colors of variables: wff set class
Syntax hints:  wa 102  wnf 1394  wcel 1438  ∃!weu 1948  ∃!wreu 2361
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-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-eu 1951  df-reu 2366
This theorem is referenced by:  riota2df  5610
  Copyright terms: Public domain W3C validator