Description: Bigcup maps the universe onto itself. (Contributed by Scott Fenton, 16-Apr-2012)
Ref | Expression | ||
---|---|---|---|
Assertion | fobigcup | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniexg | |
|
2 | 1 | rgen | |
3 | dfbigcup2 | |
|
4 | 3 | mptfng | |
5 | 2 4 | mpbi | |
6 | 3 | rnmpt | |
7 | vex | |
|
8 | vsnex | |
|
9 | unisnv | |
|
10 | 9 | eqcomi | |
11 | unieq | |
|
12 | 11 | rspceeqv | |
13 | 8 10 12 | mp2an | |
14 | 7 13 | 2th | |
15 | 14 | eqabi | |
16 | 6 15 | eqtr4i | |
17 | df-fo | |
|
18 | 5 16 17 | mpbir2an | |