Definition df-propimp 38552

Description: The implication between two sentences of propositional calculus is encoded by concatenating the two sentences and appending a two at the end. (Contributed by Thomas van Maaren, 21-Aug-2026.)

Assertion

Ref	Expression
df-propimp	⊢ prop→ = (𝑥 ∈ V, 𝑦 ∈ V ↦ ((𝑥 ++ 𝑦) ++ ⟨“2”⟩))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-propimp

Step	Hyp	Ref	Expression
1		cpropimp 38549	. 2 class prop→
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cvv 3450	. . 3 class V
5	2	cv 1569	. . . . 5 class 𝑥
6	3	cv 1569	. . . . 5 class 𝑦
7		cconcat 14668	. . . . 5 class ++
8	5, 6, 7	co 7409	. . . 4 class (𝑥 ++ 𝑦)
9		c2 12352	. . . . 5 class 2
10	9	cs1 14695	. . . 4 class ⟨“2”⟩
11	8, 10, 7	co 7409	. . 3 class ((𝑥 ++ 𝑦) ++ ⟨“2”⟩)
12	2, 3, 4, 4, 11	cmpo 7411	. 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ ((𝑥 ++ 𝑦) ++ ⟨“2”⟩))
13	1, 12	wceq 1570	1 wff prop→ = (𝑥 ∈ V, 𝑦 ∈ V ↦ ((𝑥 ++ 𝑦) ++ ⟨“2”⟩))

This definition is used by: (None)