Description: A subclass of a set is a set. Exercise 3 of TakeutiZaring p. 22. This is one way to express the Axiom of Separation ax-sep (a.k.a. Subset Axiom). (Contributed by NM, 27-Apr-1994) (Proof shortened by BJ, 18-Jul-2026)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | ssex.1 | |- B e. _V |
|
| Assertion | ssex | |- ( A C_ B -> A e. _V ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ssex.1 | |- B e. _V |
|
| 2 | ssexg | |- ( ( A C_ B /\ B e. _V ) -> A e. _V ) |
|
| 3 | 1 2 | mpan2 | |- ( A C_ B -> A e. _V ) |