Description: Distributive law for Cartesian product over indexed union. (Contributed by Mario Carneiro, 27-Apr-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | xpiundi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom | |
|
2 | eliun | |
|
3 | 2 | anbi1i | |
4 | 3 | exbii | |
5 | df-rex | |
|
6 | df-rex | |
|
7 | 6 | rexbii | |
8 | rexcom4 | |
|
9 | r19.41v | |
|
10 | 9 | exbii | |
11 | 7 8 10 | 3bitri | |
12 | 4 5 11 | 3bitr4i | |
13 | 12 | rexbii | |
14 | elxp2 | |
|
15 | 14 | rexbii | |
16 | 1 13 15 | 3bitr4i | |
17 | elxp2 | |
|
18 | eliun | |
|
19 | 16 17 18 | 3bitr4i | |
20 | 19 | eqriv | |