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	$$⊢B\in V\to ⟨“AB”⟩\left(1\right)=B$$

Proof

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