Theorem pssexg

Description: The proper subset of a set is also a set. (Contributed by Steven Nguyen, 17-Jul-2022)

	Ref	Expression
Assertion	pssexg	$$⊢\left(A\subset B\wedge B\in C\right)\to A\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		pssss	$$⊢A\subset B\to A\subseteq B$$
2		ssexg	$$⊢\left(A\subseteq B\wedge B\in C\right)\to A\in \mathrm{V}$$
3	1 2	sylan	$$⊢\left(A\subset B\wedge B\in C\right)\to A\in \mathrm{V}$$