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