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Theorem nfrmo1 3249
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 3058 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
2 nfmo1 2618 . 2 𝑥∃*𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1928 1 𝑥∃*𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 383  wnf 1857  wcel 2139  ∃*wmo 2608  ∃*wrmo 3053
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-11 2183  ax-12 2196
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-eu 2611  df-mo 2612  df-rmo 3058
This theorem is referenced by:  nfdisj1  4785  2reu3  41712
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