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Theorem nfrmo1 3358
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 3133 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
2 nfmo1 2640 . 2 𝑥∃*𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1853 1 𝑥∃*𝑥𝐴 𝜑
Colors of variables: wff setvar class
Syntax hints:  wa 398  wnf 1784  wcel 2114  ∃*wmo 2620  ∃*wrmo 3128
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-11 2161  ax-12 2177
This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1781  df-nf 1785  df-mo 2622  df-rmo 3133
This theorem is referenced by:  nfdisj1  5021  2reu3  43457
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