Metamath Proof Explorer


Theorem nfrmo1

Description: The setvar x is not free in E* x e. A ph . (Contributed by NM, 16-Jun-2017)

Ref Expression
Assertion nfrmo1 ⊢ Ⅎ x ∃* x ∈ A φ

Proof

Step Hyp Ref Expression
1 df-rmo ⊢ ∃* x ∈ A φ ↔ ∃* x x ∈ A ∧ φ
2 nfmo1 ⊢ Ⅎ x ∃* x x ∈ A ∧ φ
3 1 2 nfxfr ⊢ Ⅎ x ∃* x ∈ A φ