Metamath Proof Explorer


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