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Theorem nfreu1 3351
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 3137 . 2 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥(𝑥𝐴𝜑))
2 nfeu1 2673 . 2 𝑥∃!𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1854 1 𝑥∃!𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 399  wnf 1785  wcel 2114  ∃!weu 2652  ∃!wreu 3132
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2178
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-mo 2622  df-eu 2653  df-reu 3137
This theorem is referenced by:  riota2df  7121  2reu8  43608  iccpartdisj  43894
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