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Theorem nfreu1 3212
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 3021 . 2 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥(𝑥𝐴𝜑))
2 nfeu1 2581 . 2 𝑥∃!𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1892 1 𝑥∃!𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 383  wnf 1821  wcel 2103  ∃!weu 2571  ∃!wreu 3016
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-10 2132  ax-11 2147  ax-12 2160
This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1818  df-nf 1823  df-eu 2575  df-reu 3021
This theorem is referenced by:  riota2df  6746  2reu8  41615  iccpartdisj  41800
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