Metamath Proof Explorer

Theorem ccat2s1fst

Description: The first symbol of the concatenation of a word with two single symbols. (Contributed by Alexander van der Vekens, 22-Sep-2018) (Revised by AV, 28-Jan-2024)

		Ref	Expression
	Assertion	ccat2s1fst	$⊢ (W \in Word V \land 0 < \|W\|) \to ((W ++ ⟨“ X ”⟩) ++ ⟨“ Y ”⟩) (0) = W (0)$

Proof

Step	Hyp	Ref	Expression
1		0nn0	$⊢ 0 \in ℕ_{0}$
2		ccat2s1fvw	$⊢ (W \in Word V \land 0 \in ℕ_{0} \land 0 < \|W\|) \to ((W ++ ⟨“ X ”⟩) ++ ⟨“ Y ”⟩) (0) = W (0)$
3	1 2	mp3an2	$⊢ (W \in Word V \land 0 < \|W\|) \to ((W ++ ⟨“ X ”⟩) ++ ⟨“ Y ”⟩) (0) = W (0)$