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	Could not format assertion : No typesetting found for |- ( _Left ` A ) C_ No with typecode |-

Proof

Step	Hyp	Ref	Expression
1		leftssold	Could not format ( _Left ` A ) C_ ( _Old ` ( bday ` A ) ) : No typesetting found for |- ( _Left ` A ) C_ ( _Old ` ( bday ` A ) ) with typecode |-
2		oldssno	$$⊢\mathrm{Old}\left(\mathrm{bday}\left(A\right)\right)\subseteq \mathrm{No}$$
3	1 2	sstri	Could not format ( _Left ` A ) C_ No : No typesetting found for |- ( _Left ` A ) C_ No with typecode |-