Metamath Proof Explorer


Definition df-gdlop3

Description: Define the third Gödel operation. This function takes two arguments and returns the first argument minus the second argument (see df-dif ). Based on the third case of Definition 14.2 of TakeutiZaring p. 144. (Contributed by BTernaryTau, 2-Sep-2026)

Ref Expression
Assertion df-gdlop3 Could not format assertion : No typesetting found for |- ~F3 = ( x e. _V , y e. _V |-> ( x \ y ) ) with typecode |-

Detailed syntax breakdown

Step Hyp Ref Expression
0 cgdlop3 Could not format ~F3 : No typesetting found for class ~F3 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 cdif class x ∖ y
7 1 3 2 2 6 cmpo class x ∈ V , y ∈ V ⟼ x ∖ y
8 0 7 wceq Could not format ~F3 = ( x e. _V , y e. _V |-> ( x \ y ) ) : No typesetting found for wff ~F3 = ( x e. _V , y e. _V |-> ( x \ y ) ) with typecode wff