Theorem s2fv0

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

	Ref	Expression
Assertion	s2fv0	$$⊢A\in V\to ⟨“AB”⟩\left(0\right)=A$$

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		s1fv	$$⊢A\in V\to ⟨“A”⟩\left(0\right)=A$$
5		0nn0	$$⊢0\in {\mathbb{N}}_0$$
6		0lt1	$$⊢0<1$$
7	1 2 3 4 5 6	cats1fv	$$⊢A\in V\to ⟨“AB”⟩\left(0\right)=A$$