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 ∈ Word 𝑉 → 𝑊 ∈ Word V )

Proof

Step	Hyp	Ref	Expression
1		ssv	⊢ 𝑉 ⊆ V
2		sswrd	⊢ ( 𝑉 ⊆ V → Word 𝑉 ⊆ Word V )
3	1 2	ax-mp	⊢ Word 𝑉 ⊆ Word V
4	3	sseli	⊢ ( 𝑊 ∈ Word 𝑉 → 𝑊 ∈ Word V )