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Metamath Proof Explorer

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	$⊢ W \in Word V \to W \in Word V$

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