Metamath Proof Explorer

Theorem ssltex2

Description: The second argument of surreal set less-than exists. (Contributed by Scott Fenton, 8-Dec-2021)

Ref Expression
Assertion ssltex2 ⊢A≪sB→B∈V

Proof

Step Hyp Ref Expression
1 brsslt ⊢A≪sB↔A∈V∧B∈V∧A⊆No∧B⊆No∧∀x∈A∀y∈Bx<sy
2 simplr ⊢A∈V∧B∈V∧A⊆No∧B⊆No∧∀x∈A∀y∈Bx<sy→B∈V
3 1 2 sylbi ⊢A≪sB→B∈V