Theorem nfrmo1 3395

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 3368	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfmo1 2585	. 2 ⊢ Ⅎ𝑥∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)
3	1, 2	nfxfr 1885	1 ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑

This proof depends on syntax axioms:   ∧ wa 401  Ⅎwnf 1815   ∈ wcel 2146  ∃*wmo 2565  ∃*wrmo 3367

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-10 2179  ax-11 2196

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-nf 1816  df-mo 2567  df-rmo 3368

This theorem is used by:  nfdisj1  5086  2reu3  48320