Theorem prelpwi

Description: If two sets are members of a class, then the unordered pair of those two sets is a member of the powerclass of that class. (Contributed by Thierry Arnoux, 10-Mar-2017) (Proof shortened by AV, 23-Oct-2021)

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

Proof

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