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Theorem nfreu1 3104
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 2915 . 2 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥(𝑥𝐴𝜑))
2 nfeu1 2479 . 2 𝑥∃!𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1776 1 𝑥∃!𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 384  wnf 1705  wcel 1987  ∃!weu 2469  ∃!wreu 2910
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-11 2031  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1702  df-nf 1707  df-eu 2473  df-reu 2915
This theorem is referenced by:  riota2df  6596  2reu8  40526  iccpartdisj  40701
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