Theorem moani

Description: "At most one" is still true when a conjunct is added. (Contributed by NM, 9-Mar-1995)

	Ref	Expression
Hypothesis	moani.1	⊢ ∃* 𝑥 𝜑
Assertion	moani	⊢ ∃* 𝑥 ( 𝜓 ∧ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		moani.1	⊢ ∃* 𝑥 𝜑
2		moan	⊢ ( ∃* 𝑥 𝜑 → ∃* 𝑥 ( 𝜓 ∧ 𝜑 ) )
3	1 2	ax-mp	⊢ ∃* 𝑥 ( 𝜓 ∧ 𝜑 )