Theorem elsnd

Description: There is at most one element in a singleton. (Contributed by Thierry Arnoux, 13-Oct-2025)

	Ref	Expression
Hypothesis	elsnd.1	$$⊢\phi \to A\in \left\{B\right\}$$
Assertion	elsnd	$$⊢\phi \to A=B$$

Proof

Step	Hyp	Ref	Expression
1		elsnd.1	$$⊢\phi \to A\in \left\{B\right\}$$
2		elsni	$$⊢A\in \left\{B\right\}\to A=B$$
3	1 2	syl	$$⊢\phi \to A=B$$