Theorem leftlt

Description: A member of a surreal's left set is less than it. (Contributed by Scott Fenton, 7-Nov-2025)

	Ref	Expression
Assertion	leftlt	$$⊢A\in L\left(B\right)\to A{<}_{s}B$$

Proof

Step	Hyp	Ref	Expression
1		elleft	$$⊢A\in L\left(B\right)\leftrightarrow \left(A\in \mathrm{Old}\left(\mathrm{bday}\left(B\right)\right)\wedge A{<}_{s}B\right)$$
2	1	simprbi	$$⊢A\in L\left(B\right)\to A{<}_{s}B$$