Theorem wrdv

Description: A word over an alphabet is a word over the universal class. (Contributed by AV, 8-Feb-2021) (Proof shortened by JJ, 18-Nov-2022)

	Ref	Expression
Assertion	wrdv	$$⊢W\in \mathrm{Word}V\to W\in \mathrm{Word}\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ssv	$$⊢V\subseteq \mathrm{V}$$
2		sswrd	$$⊢V\subseteq \mathrm{V}\to \mathrm{Word}V\subseteq \mathrm{Word}\mathrm{V}$$
3	1 2	ax-mp	$$⊢\mathrm{Word}V\subseteq \mathrm{Word}\mathrm{V}$$
4	3	sseli	$$⊢W\in \mathrm{Word}V\to W\in \mathrm{Word}\mathrm{V}$$