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Metamath Proof Explorer

Theorem ovsn

Description: The operation value of a singleton of a nested ordered pair is the last member. (Contributed by Zhi Wang, 22-Oct-2025)

		Ref	Expression
	Hypothesis	ovsn.1	$⊢ C \in V$
	Assertion	ovsn	$⊢ A \{⟨⟨A, B⟩, C⟩\} B = C$

Step	Hyp	Ref	Expression
1		ovsn.1	$⊢ C \in V$
2		ovsng	$⊢ C \in V \to A \{⟨⟨A, B⟩, C⟩\} B = C$
3	1 2	ax-mp	$⊢ A \{⟨⟨A, B⟩, C⟩\} B = C$