Theorem rightoldd

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

	Ref	Expression
Hypothesis	rightel.1	$$⊢\phi \to A\in R\left(B\right)$$
Assertion	rightoldd	$$⊢\phi \to A\in \mathrm{Old}\left(\mathrm{bday}\left(B\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		rightel.1	$$⊢\phi \to A\in R\left(B\right)$$
2		rightold	$$⊢A\in R\left(B\right)\to A\in \mathrm{Old}\left(\mathrm{bday}\left(B\right)\right)$$
3	1 2	syl	$$⊢\phi \to A\in \mathrm{Old}\left(\mathrm{bday}\left(B\right)\right)$$