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

Theorem nfreu1 2662
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 2475 . 2 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥(𝑥𝐴𝜑))
2 nfeu1 2049 . 2 𝑥∃!𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1485 1 𝑥∃!𝑥𝐴 𝜑
Colors of variables: wff set class
Syntax hints:  wa 104  wnf 1471  ∃!weu 2038  wcel 2160  ∃!wreu 2470
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-eu 2041  df-reu 2475
This theorem is referenced by:  riota2df  5873
  Copyright terms: Public domain W3C validator