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Theorem nfrmo1 3241
Description: The setvar 𝑥 is not free in ∃*𝑥𝐴𝜑. (Contributed by NM, 16-Jun-2017.)
Assertion
Ref Expression
nfrmo1 𝑥∃*𝑥𝐴 𝜑

Proof of Theorem nfrmo1
StepHypRef Expression
1 df-rmo 3050 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
2 nfmo1 2610 . 2 𝑥∃*𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1920 1 𝑥∃*𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 383  wnf 1849  wcel 2131  ∃*wmo 2600  ∃*wrmo 3045
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046  ax-7 2082  ax-10 2160  ax-11 2175  ax-12 2188
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1846  df-nf 1851  df-eu 2603  df-mo 2604  df-rmo 3050
This theorem is referenced by:  nfdisj1  4777  2reu3  41686
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