Description: A sigma-algebra contains the empty set. (Contributed by Thierry Arnoux, 4-Sep-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | 0elsiga | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isrnsiga | |
|
2 | 1 | simprbi | |
3 | 3simpa | |
|
4 | 3 | adantl | |
5 | 4 | eximi | |
6 | difeq2 | |
|
7 | difid | |
|
8 | 6 7 | eqtrdi | |
9 | 8 | eleq1d | |
10 | 9 | rspcva | |
11 | 10 | exlimiv | |
12 | 2 5 11 | 3syl | |