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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 ∈ V
	Assertion	rnsnop	⊢ ran { ⟨ 𝐴 , 𝐵 ⟩ } = { 𝐵 }

Proof

Step	Hyp	Ref	Expression
1		cnvsn.1	⊢ 𝐴 ∈ V
2		rnsnopg	⊢ ( 𝐴 ∈ V → ran { ⟨ 𝐴 , 𝐵 ⟩ } = { 𝐵 } )
3	1 2	ax-mp	⊢ ran { ⟨ 𝐴 , 𝐵 ⟩ } = { 𝐵 }