Metamath Proof Explorer


Theorem ssltex1

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

Ref Expression
Assertion ssltex1 A s B A V

Proof

Step Hyp Ref Expression
1 brsslt A s B A V B V A No B No x A y B x < s y
2 simpll A V B V A No B No x A y B x < s y A V
3 1 2 sylbi A s B A V