Metamath Proof Explorer


Definition df-propneg

Description: The negation of a sentence of propositional calculus is encoded by appending a one after the sentence. (Contributed by Thomas van Maaren, 21-Aug-2026)

Ref Expression
Assertion df-propneg prop¬ = ( 𝑥 ∈ V ↦ ( 𝑥 ++ ⟨“ 1 ”⟩ ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cpropneg ⊢ prop¬
1 vx ⊢ 𝑥
2 cvv ⊢ V
3 1 cv ⊢ 𝑥
4 cconcat ⊢ ++
5 c1 ⊢ 1
6 5 cs1 ⊢ ⟨“ 1 ”⟩
7 3 6 4 co ⊢ ( 𝑥 ++ ⟨“ 1 ”⟩ )
8 1 2 7 cmpt ⊢ ( 𝑥 ∈ V ↦ ( 𝑥 ++ ⟨“ 1 ”⟩ ) )
9 0 8 wceq ⊢ prop¬ = ( 𝑥 ∈ V ↦ ( 𝑥 ++ ⟨“ 1 ”⟩ ) )