Theorem nfrmo1 3396

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 3369	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfmo1 2585	. 2 ⊢ Ⅎ𝑥∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)
3	1, 2	nfxfr 1886	1 ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑

This proof depends on syntax axioms:   ∧ wa 401  Ⅎwnf 1816   ∈ wcel 2147  ∃*wmo 2565  ∃*wrmo 3368

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-10 2180  ax-11 2197

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-nf 1817  df-mo 2567  df-rmo 3369

This theorem is used by:  nfdisj1  5089  2reu3  48454