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Metamath Proof Explorer

Theorem moor

Description: "At most one" is still the case when a disjunct is removed. (Contributed by NM, 5-Apr-2004)

Ref Expression
Assertion moor ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ∃* 𝑥 𝜑 )

Proof

Step Hyp Ref Expression
1 orc ⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ) )
2 1 moimi ⊢ ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ∃* 𝑥 𝜑 )