Description: Indexed union of intersection. Generalization of half of theorem "Distributive laws" in Enderton p. 30. Use uniiun to recover Enderton's theorem. (Contributed by NM, 26-Mar-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | iunin2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.42v | |
|
2 | elin | |
|
3 | 2 | rexbii | |
4 | eliun | |
|
5 | 4 | anbi2i | |
6 | 1 3 5 | 3bitr4i | |
7 | eliun | |
|
8 | elin | |
|
9 | 6 7 8 | 3bitr4i | |
10 | 9 | eqriv | |