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Metamath Proof Explorer

Theorem s4fv3

Description: Extract the fourth symbol from a length 4 string. (Contributed by Thierry Arnoux, 8-Oct-2020)

Ref Expression
Assertion s4fv3 ⊢ D ∈ V → ⟨“ ABCD ”⟩ ⁡ 3 = D

Proof

Step Hyp Ref Expression
1 df-s4 ⊢ ⟨“ ABCD ”⟩ = ⟨“ ABC ”⟩ ++ ⟨“ D ”⟩
2 s3cli ⊢ ⟨“ ABC ”⟩ ∈ Word V
3 s3len ⊢ ⟨“ ABC ”⟩ = 3
4 1 2 3 cats1fvn ⊢ D ∈ V → ⟨“ ABCD ”⟩ ⁡ 3 = D