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Metamath Proof Explorer

Theorem s2fv1

Description: Extract the second symbol from a doubleton word. (Contributed by Stefan O'Rear, 23-Aug-2015) (Revised by Mario Carneiro, 26-Feb-2016)

		Ref	Expression
	Assertion	s2fv1	$⊢ B \in V \to ⟨“ A B ”⟩ (1) = B$

Proof

Step	Hyp	Ref	Expression
1		df-s2	$⊢ ⟨“ A B ”⟩ = ⟨“ A ”⟩ ++ ⟨“ B ”⟩$
2		s1cli	$⊢ ⟨“ A ”⟩ \in Word V$
3		s1len	$⊢ \|⟨“ A ”⟩\| = 1$
4	1 2 3	cats1fvn	$⊢ B \in V \to ⟨“ A B ”⟩ (1) = B$