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Theorem nfreu1 3089
Description: The setvar 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 2903 . 2 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥(𝑥𝐴𝜑))
2 nfeu1 2468 . 2 𝑥∃!𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1771 1 𝑥∃!𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 383  wnf 1699  wcel 1977  ∃!weu 2458  ∃!wreu 2898
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701  df-eu 2462  df-reu 2903
This theorem is referenced by:  riota2df  6531  2reu8  39841  iccpartdisj  39975
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