Metamath Proof Explorer


Definition df-propvar

Description: Variables in sentences of propositional calculus are encoded by appending a zero after the number of the variable. (Contributed by Thomas van Maaren, 21-Aug-2026)

Ref Expression
Assertion df-propvar propvar = ( 𝑛 ∈ ℕ ↦ ( ⟨“ 𝑛 ”⟩ ++ ⟨“ 0 ”⟩ ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cpropvar ⊢ propvar
1 vn ⊢ 𝑛
2 cn ⊢ ℕ
3 1 cv ⊢ 𝑛
4 3 cs1 ⊢ ⟨“ 𝑛 ”⟩
5 cconcat ⊢ ++
6 cc0 ⊢ 0
7 6 cs1 ⊢ ⟨“ 0 ”⟩
8 4 7 5 co ⊢ ( ⟨“ 𝑛 ”⟩ ++ ⟨“ 0 ”⟩ )
9 1 2 8 cmpt ⊢ ( 𝑛 ∈ ℕ ↦ ( ⟨“ 𝑛 ”⟩ ++ ⟨“ 0 ”⟩ ) )
10 0 9 wceq ⊢ propvar = ( 𝑛 ∈ ℕ ↦ ( ⟨“ 𝑛 ”⟩ ++ ⟨“ 0 ”⟩ ) )