Theorem ssltex1

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

	Ref	Expression
Assertion	ssltex1	|- ( A < A e. _V )

Proof

Step	Hyp	Ref	Expression
1		brsslt	|- ( A < ( ( A e. _V /\ B e. _V ) /\ ( A C_ No /\ B C_ No /\ A. x e. A A. y e. B x
2		simpll	|- ( ( ( A e. _V /\ B e. _V ) /\ ( A C_ No /\ B C_ No /\ A. x e. A A. y e. B x A e. _V )
3	1 2	sylbi	|- ( A < A e. _V )