Theorem elsnd

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

	Ref	Expression
Hypothesis	elsnd.1	⊢ ( 𝜑 → 𝐴 ∈ { 𝐵 } )
Assertion	elsnd	⊢ ( 𝜑 → 𝐴 = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		elsnd.1	⊢ ( 𝜑 → 𝐴 ∈ { 𝐵 } )
2		elsni	⊢ ( 𝐴 ∈ { 𝐵 } → 𝐴 = 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 = 𝐵 )