Theorem leftssno

Description: The left set of a surreal number is a subset of the surreals. (Contributed by Scott Fenton, 9-Oct-2024)

	Ref	Expression
Assertion	leftssno	$$⊢L\left(A\right)\subseteq \mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		leftssold	$$⊢L\left(A\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(A\right)\right)$$
2		oldssno	$$⊢\mathrm{Old}\left(\mathrm{bday}\left(A\right)\right)\subseteq \mathrm{No}$$
3	1 2	sstri	$$⊢L\left(A\right)\subseteq \mathrm{No}$$