Theorem prssi

Description: A pair of elements of a class is a subset of the class. (Contributed by NM, 16-Jan-2015)

	Ref	Expression
Assertion	prssi	$$⊢\left(A\in C\wedge B\in C\right)\to \left\{A,B\right\}\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		prssg	$$⊢\left(A\in C\wedge B\in C\right)\to \left(\left(A\in C\wedge B\in C\right)\leftrightarrow \left\{A,B\right\}\subseteq C\right)$$
2	1	ibi	$$⊢\left(A\in C\wedge B\in C\right)\to \left\{A,B\right\}\subseteq C$$