Theorem leftoldd

Description: An element of a left set is an element of the old set. (Contributed by Scott Fenton, 27-Feb-2026)

	Ref	Expression
Hypothesis	leftel.1	|- ( ph -> A e. ( _Left ` B ) )
Assertion	leftoldd	|- ( ph -> A e. ( _Old ` ( bday ` B ) ) )

Proof

Step	Hyp	Ref	Expression
1		leftel.1	|- ( ph -> A e. ( _Left ` B ) )
2		leftold	|- ( A e. ( _Left ` B ) -> A e. ( _Old ` ( bday ` B ) ) )
3	1 2	syl	|- ( ph -> A e. ( _Old ` ( bday ` B ) ) )