Theorem eltpi

Description: A member of an unordered triple of classes is one of them. (Contributed by Mario Carneiro, 11-Feb-2015)

	Ref	Expression
Assertion	eltpi	$$⊢A\in \left\{B,C,D\right\}\to \left(A=B\vee A=C\vee A=D\right)$$

Proof

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