Metamath Proof Explorer


Theorem moan

Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995)

Ref Expression
Assertion moan ( ∃* 𝑥 𝜑 → ∃* 𝑥 ( 𝜓𝜑 ) )

Proof

Step Hyp Ref Expression
1 simpr ( ( 𝜓𝜑 ) → 𝜑 )
2 1 moimi ( ∃* 𝑥 𝜑 → ∃* 𝑥 ( 𝜓𝜑 ) )