New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > df-cup | GIF version |
Description: Define the cup function. (Contributed by SF, 9-Feb-2015.) |
Ref | Expression |
---|---|
df-cup | ⊢ Cup = (x ∈ V, y ∈ V ↦ (x ∪ y)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccup 5741 | . 2 class Cup | |
2 | vx | . . 3 setvar x | |
3 | vy | . . 3 setvar y | |
4 | cvv 2859 | . . 3 class V | |
5 | 2 | cv 1641 | . . . 4 class x |
6 | 3 | cv 1641 | . . . 4 class y |
7 | 5, 6 | cun 3207 | . . 3 class (x ∪ y) |
8 | 2, 3, 4, 4, 7 | cmpt2 5653 | . 2 class (x ∈ V, y ∈ V ↦ (x ∪ y)) |
9 | 1, 8 | wceq 1642 | 1 wff Cup = (x ∈ V, y ∈ V ↦ (x ∪ y)) |
Colors of variables: wff setvar class |
This definition is referenced by: cupvalg 5812 fncup 5813 cupex 5816 |
Copyright terms: Public domain | W3C validator |