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Theorem nfrmo1 3258
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 3063 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
2 nfmo1 2570 . 2 𝑥∃*𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1948 1 𝑥∃*𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 384  wnf 1878  wcel 2155  ∃*wmo 2563  ∃*wrmo 3058
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-10 2183  ax-11 2198  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-or 874  df-ex 1875  df-nf 1879  df-mo 2565  df-rmo 3063
This theorem is referenced by:  nfdisj1  4792  2reu3  41883
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