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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 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 ”⟩ ‘ 1 ) = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		df-s2	⊢ ⟨“ 𝐴 𝐵 ”⟩ = ( ⟨“ 𝐴 ”⟩ ++ ⟨“ 𝐵 ”⟩ )
2		s1cli	⊢ ⟨“ 𝐴 ”⟩ ∈ Word V
3		s1len	⊢ ( ♯ ‘ ⟨“ 𝐴 ”⟩ ) = 1
4	1 2 3	cats1fvn	⊢ ( 𝐵 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 ”⟩ ‘ 1 ) = 𝐵 )