Theorem nrexrmo

Description: Nonexistence implies restricted "at most one". (Contributed by NM, 17-Jun-2017)

	Ref	Expression
Assertion	nrexrmo	$$⊢\neg \exists x\in A\phi \to {\exists }^{*}x\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \exists x\in A\phi \to \left(\exists x\in A\phi \to \exists !x\in A\phi \right)$$
2		rmo5	$$⊢{\exists }^{*}x\in A\phi \leftrightarrow \left(\exists x\in A\phi \to \exists !x\in A\phi \right)$$
3	1 2	sylibr	$$⊢\neg \exists x\in A\phi \to {\exists }^{*}x\in A\phi$$