Theorem bj-elsn12g

Description: Join of elsng and elsn2g . (Contributed by BJ, 18-Nov-2023)

	Ref	Expression
Assertion	bj-elsn12g	⊢ ( ( 𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊 ) → ( 𝐴 ∈ { 𝐵 } ↔ 𝐴 = 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		elsng	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∈ { 𝐵 } ↔ 𝐴 = 𝐵 ) )
2		elsn2g	⊢ ( 𝐵 ∈ 𝑊 → ( 𝐴 ∈ { 𝐵 } ↔ 𝐴 = 𝐵 ) )
3	1 2	jaoi	⊢ ( ( 𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊 ) → ( 𝐴 ∈ { 𝐵 } ↔ 𝐴 = 𝐵 ) )