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 | |- ~F3 = ( x e. _V , y e. _V |-> ( x \ y ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cgdlop3 | |- ~F3 |
|
| 1 | vx | |- x |
|
| 2 | cvv | |- _V |
|
| 3 | vy | |- y |
|
| 4 | 1 | cv | |- x |
| 5 | 3 | cv | |- y |
| 6 | 4 5 | cdif | |- ( x \ y ) |
| 7 | 1 3 2 2 6 | cmpo | |- ( x e. _V , y e. _V |-> ( x \ y ) ) |
| 8 | 0 7 | wceq | |- ~F3 = ( x e. _V , y e. _V |-> ( x \ y ) ) |