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Metamath Proof Explorer

Theorem rnsnop

Description: The range of a singleton of an ordered pair is the singleton of the second member. (Contributed by NM, 24-Jul-2004) (Revised by Mario Carneiro, 26-Apr-2015)

		Ref	Expression
	Hypothesis	cnvsn.1	$⊢ A \in V$
	Assertion	rnsnop	$⊢ ran \{⟨A, B⟩\} = \{B\}$

Proof

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