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 ( 𝜓 ∧ 𝜑 ) )

Proof

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