Metamath Proof Explorer


Theorem dfmo

Description: Simplify definition df-mo by removing its provable hypothesis. (Contributed by Wolf Lammen, 15-Feb-2026)

Ref Expression
Assertion dfmo ( ∃* 𝑥 𝜑 ↔ ∃ 𝑦 ∀ 𝑥 ( 𝜑 → 𝑥 = 𝑦 ) )

Proof

Step Hyp Ref Expression
1 mojust ⊢ ( ∃ 𝑦 ∀ 𝑥 ( 𝜑 → 𝑥 = 𝑦 ) ↔ ∃ 𝑧 ∀ 𝑥 ( 𝜑 → 𝑥 = 𝑧 ) )
2 1 df-mo ⊢ ( ∃* 𝑥 𝜑 ↔ ∃ 𝑦 ∀ 𝑥 ( 𝜑 → 𝑥 = 𝑦 ) )