Metamath Proof Explorer

Theorem ccatws1clv

Description: The concatenation of a word with a singleton word (which can be over a different alphabet) is a word. (Contributed by AV, 5-Mar-2022)

		Ref	Expression
	Assertion	ccatws1clv	$⊢ W \in Word V \to W ++ ⟨“ X ”⟩ \in Word V$

Proof

Step	Hyp	Ref	Expression
1		wrdv	$⊢ W \in Word V \to W \in Word V$
2		s1cli	$⊢ ⟨“ X ”⟩ \in Word V$
3		ccatcl	$⊢ (W \in Word V \land ⟨“ X ”⟩ \in Word V) \to W ++ ⟨“ X ”⟩ \in Word V$
4	1 2 3	sylancl	$⊢ W \in Word V \to W ++ ⟨“ X ”⟩ \in Word V$