Description: Define the second Gödel operation. This function takes two arguments and returns the intersection of the first argument with the membership relation (see df-in and df-eprel ). The second argument is ignored. Based on the second case of Definition 14.2 of TakeutiZaring p. 144. (Contributed by BTernaryTau, 2-Sep-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-gdlop2 | |- ~F2 = ( x e. _V , y e. _V |-> ( x i^i _E ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cgdlop2 | |- ~F2 |
|
| 1 | vx | |- x |
|
| 2 | cvv | |- _V |
|
| 3 | vy | |- y |
|
| 4 | 1 | cv | |- x |
| 5 | cep | |- _E |
|
| 6 | 4 5 | cin | |- ( x i^i _E ) |
| 7 | 1 3 2 2 6 | cmpo | |- ( x e. _V , y e. _V |-> ( x i^i _E ) ) |
| 8 | 0 7 | wceq | |- ~F2 = ( x e. _V , y e. _V |-> ( x i^i _E ) ) |