Metamath Proof Explorer


Theorem ssexi

Description: A subclass of a set is a set. (Contributed by NM, 9-Sep-1993)

Ref Expression
Hypotheses ssexi.1 ⊢ 𝐵 ∈ V
ssexi.2 ⊢ 𝐴 ⊆ 𝐵
Assertion ssexi 𝐴 ∈ V

Proof

Step Hyp Ref Expression
1 ssexi.1 ⊢ 𝐵 ∈ V
2 ssexi.2 ⊢ 𝐴 ⊆ 𝐵
3 1 ssex ⊢ ( 𝐴 ⊆ 𝐵 → 𝐴 ∈ V )
4 2 3 ax-mp ⊢ 𝐴 ∈ V