Theorem nfrmo1 3111

Description: The setvar 𝑥 is not free in ∃*𝑥 ∈ 𝐴𝜑. (Contributed by NM, 16-Jun-2017.)

Assertion

Ref	Expression
nfrmo1	⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑

Proof of Theorem nfrmo1

Step	Hyp	Ref	Expression
1		df-rmo 2920	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfmo1 2481	. 2 ⊢ Ⅎ𝑥∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)
3	1, 2	nfxfr 1779	1 ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑

Syntax hints:   ∧ wa 384  Ⅎwnf 1708   ∈ wcel 1990  ∃*wmo 2471  ∃*wrmo 2915

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475  df-rmo 2920

This theorem is referenced by:  nfdisj1  4633  2reu3  41188