Metamath Proof Explorer


Definition df-gdlop7

Description: Define the seventh Gödel operation. This function takes two arguments and returns the intersection of the first argument with the second converse of the second argument (see df-in and df-cnv2 ). Based on the seventh case of Definition 14.2 of TakeutiZaring p. 144. (Contributed by BTernaryTau, 2-Sep-2026)

Ref Expression
Assertion df-gdlop7 Could not format assertion : No typesetting found for |- ~F7 = ( x e. _V , y e. _V |-> ( x i^i ( Cnv2 ` y ) ) ) with typecode |-

Detailed syntax breakdown

Step Hyp Ref Expression
0 cgdlop7 Could not format ~F7 : No typesetting found for class ~F7 with typecode class
1 vx setvar x
2 cvv class V
3 vy setvar y
4 1 cv setvar x
5 ccnv2 Could not format Cnv2 : No typesetting found for class Cnv2 with typecode class
6 3 cv setvar y
7 6 5 cfv Could not format ( Cnv2 ` y ) : No typesetting found for class ( Cnv2 ` y ) with typecode class
8 4 7 cin Could not format ( x i^i ( Cnv2 ` y ) ) : No typesetting found for class ( x i^i ( Cnv2 ` y ) ) with typecode class
9 1 3 2 2 8 cmpo Could not format ( x e. _V , y e. _V |-> ( x i^i ( Cnv2 ` y ) ) ) : No typesetting found for class ( x e. _V , y e. _V |-> ( x i^i ( Cnv2 ` y ) ) ) with typecode class
10 0 9 wceq Could not format ~F7 = ( x e. _V , y e. _V |-> ( x i^i ( Cnv2 ` y ) ) ) : No typesetting found for wff ~F7 = ( x e. _V , y e. _V |-> ( x i^i ( Cnv2 ` y ) ) ) with typecode wff