Theorem nexmo1

Description: If there is no case where wff is true, it is true for at most one case. (Contributed by Peter Mazsa, 27-Sep-2021)

	Ref	Expression
Assertion	nexmo1	⊢ ( ¬ ∃ 𝑥 𝜑 → ∃* 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ ∃ 𝑥 𝜑 → ( ∃ 𝑥 𝜑 → ∃! 𝑥 𝜑 ) )
2		moeu	⊢ ( ∃* 𝑥 𝜑 ↔ ( ∃ 𝑥 𝜑 → ∃! 𝑥 𝜑 ) )
3	1 2	sylibr	⊢ ( ¬ ∃ 𝑥 𝜑 → ∃* 𝑥 𝜑 )