Theorem nfrmo1 3090

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 2904	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfmo1 2469	. 2 ⊢ Ⅎ𝑥∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)
3	1, 2	nfxfr 1771	1 ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑

Syntax hints:   ∧ wa 383  Ⅎwnf 1699   ∈ wcel 1977  ∃*wmo 2459  ∃*wrmo 2899

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463  df-rmo 2904

This theorem is referenced by:  nfdisj1  4566  2reu3  39837