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	$$⊢\neg \exists x\phi \to {\exists }^{*}x\phi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \exists x\phi \to \left(\exists x\phi \to \exists !x\phi \right)$$
2		moeu	$$⊢{\exists }^{*}x\phi \leftrightarrow \left(\exists x\phi \to \exists !x\phi \right)$$
3	1 2	sylibr	$$⊢\neg \exists x\phi \to {\exists }^{*}x\phi$$