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	$$⊢A\in \left\{B,C\right\}\to \left(A=B\vee A=C\right)$$

Proof

Step	Hyp	Ref	Expression
1		elprg	$$⊢A\in \left\{B,C\right\}\to \left(A\in \left\{B,C\right\}\leftrightarrow \left(A=B\vee A=C\right)\right)$$
2	1	ibi	$$⊢A\in \left\{B,C\right\}\to \left(A=B\vee A=C\right)$$