Theorem prid2g

Description: An unordered pair contains its second member. Part of Theorem 7.6 of Quine p. 49. (Contributed by Stefan Allan, 8-Nov-2008)

	Ref	Expression
Assertion	prid2g	⊢ ( 𝐵 ∈ 𝑉 → 𝐵 ∈ { 𝐴 , 𝐵 } )

Proof

Step	Hyp	Ref	Expression
1		prid1g	⊢ ( 𝐵 ∈ 𝑉 → 𝐵 ∈ { 𝐵 , 𝐴 } )
2		prcom	⊢ { 𝐵 , 𝐴 } = { 𝐴 , 𝐵 }
3	1 2	eleqtrdi	⊢ ( 𝐵 ∈ 𝑉 → 𝐵 ∈ { 𝐴 , 𝐵 } )