Theorem elpri

Description: If a class is an element of a pair, then it is one of the two paired elements. (Contributed by Scott Fenton, 1-Apr-2011)

	Ref	Expression
Assertion	elpri	⊢ ( 𝐴 ∈ { 𝐵 , 𝐶 } → ( 𝐴 = 𝐵 ∨ 𝐴 = 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		elprg	⊢ ( 𝐴 ∈ { 𝐵 , 𝐶 } → ( 𝐴 ∈ { 𝐵 , 𝐶 } ↔ ( 𝐴 = 𝐵 ∨ 𝐴 = 𝐶 ) ) )
2	1	ibi	⊢ ( 𝐴 ∈ { 𝐵 , 𝐶 } → ( 𝐴 = 𝐵 ∨ 𝐴 = 𝐶 ) )