Theorem nfrmo1 2482

Description: 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 2314	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		nfmo1 1912	. 2 ⊢ Ⅎ𝑥∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)
3	1, 2	nfxfr 1363	1 ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑

Syntax hints:   ∧ wa 97  Ⅎwnf 1349   ∈ wcel 1393  ∃*wmo 1901  ∃*wrmo 2309

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903  df-mo 1904  df-rmo 2314

This theorem is referenced by:  nfdisj1  3758