Metamath Proof Explorer


Definition df-gdlop1

Description: Define the first Gödel operation. This function takes two arguments and returns the unordered pair containing both (see df-pr ). Based on the first case of Definition 14.2 of TakeutiZaring p. 144. (Contributed by BTernaryTau, 2-Sep-2026)

Ref Expression
Assertion df-gdlop1 Could not format assertion : No typesetting found for |- ~F1 = ( x e. _V , y e. _V |-> { x , y } ) with typecode |-

Detailed syntax breakdown

Step Hyp Ref Expression
0 cgdlop1 Could not format ~F1 : No typesetting found for class ~F1 with typecode class
1 vx setvar x
2 cvv class V
3 vy setvar y
4 1 cv setvar x
5 3 cv setvar y
6 4 5 cpr class x y
7 1 3 2 2 6 cmpo class x ∈ V , y ∈ V ⟼ x y
8 0 7 wceq Could not format ~F1 = ( x e. _V , y e. _V |-> { x , y } ) : No typesetting found for wff ~F1 = ( x e. _V , y e. _V |-> { x , y } ) with typecode wff