Theorem ssexOLD

Description: Obsolete version of ssex as of 18-Jul-2026. (Contributed by NM, 27-Apr-1994) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ssex.1	$$⊢B\in \mathrm{V}$$
Assertion	ssexOLD	$$⊢A\subseteq B\to A\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ssex.1	$$⊢B\in \mathrm{V}$$
2		dfss2	$$⊢A\subseteq B\leftrightarrow A\cap B=A$$
3	1	inex2	$$⊢A\cap B\in \mathrm{V}$$
4		eleq1	$$⊢A\cap B=A\to \left(A\cap B\in \mathrm{V}\leftrightarrow A\in \mathrm{V}\right)$$
5	3 4	mpbii	$$⊢A\cap B=A\to A\in \mathrm{V}$$
6	2 5	sylbi	$$⊢A\subseteq B\to A\in \mathrm{V}$$