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 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 ”⟩ ‘ 0 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		df-s2	⊢ ⟨“ 𝐴 𝐵 ”⟩ = ( ⟨“ 𝐴 ”⟩ ++ ⟨“ 𝐵 ”⟩ )
2		s1cli	⊢ ⟨“ 𝐴 ”⟩ ∈ Word V
3		s1len	⊢ ( ♯ ‘ ⟨“ 𝐴 ”⟩ ) = 1
4		s1fv	⊢ ( 𝐴 ∈ 𝑉 → ( ⟨“ 𝐴 ”⟩ ‘ 0 ) = 𝐴 )
5		0nn0	⊢ 0 ∈ ℕ0
6		0lt1	⊢ 0 < 1
7	1 2 3 4 5 6	cats1fv	⊢ ( 𝐴 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 ”⟩ ‘ 0 ) = 𝐴 )