Theorem leftssold

Description: The left options are a subset of the old set. (Contributed by Scott Fenton, 9-Oct-2024)

	Ref	Expression
Assertion	leftssold	Could not format assertion : No typesetting found for |- ( _Left ` X ) C_ ( _Old ` ( bday ` X ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		leftval	Could not format ( _Left ` X ) = { x e. ( _Old ` ( bday ` X ) ) | x
2		ssrab2	$$⊢\left\{x\in \mathrm{Old}\left(\mathrm{bday}\left(X\right)\right)|x{<}_{s}X\right\}\subseteq \mathrm{Old}\left(\mathrm{bday}\left(X\right)\right)$$
3	1 2	eqsstri	Could not format ( _Left ` X ) C_ ( _Old ` ( bday ` X ) ) : No typesetting found for |- ( _Left ` X ) C_ ( _Old ` ( bday ` X ) ) with typecode |-