Description: Bigcup using maps-to notation. (Contributed by Scott Fenton, 16-Apr-2012)
Ref | Expression | ||
---|---|---|---|
Assertion | dfbigcup2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relbigcup | |
|
2 | mptrel | |
|
3 | eqcom | |
|
4 | vex | |
|
5 | 4 | brbigcup | |
6 | vex | |
|
7 | eleq1w | |
|
8 | unieq | |
|
9 | 8 | eqeq2d | |
10 | 7 9 | anbi12d | |
11 | 6 | biantrur | |
12 | 10 11 | bitr4di | |
13 | eqeq1 | |
|
14 | df-mpt | |
|
15 | 6 4 12 13 14 | brab | |
16 | 3 5 15 | 3bitr4i | |
17 | 1 2 16 | eqbrriv | |