Description: The property of being an ultrafilter. (Contributed by Jeff Hankins, 30-Nov-2009) (Revised by Mario Carneiro, 29-Jul-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | isufil | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ufil | |
|
2 | pweq | |
|
3 | 2 | adantr | |
4 | eleq2 | |
|
5 | 4 | adantl | |
6 | difeq1 | |
|
7 | eleq12 | |
|
8 | 6 7 | sylan | |
9 | 5 8 | orbi12d | |
10 | 3 9 | raleqbidv | |
11 | fveq2 | |
|
12 | fvex | |
|
13 | elfvdm | |
|
14 | 1 10 11 12 13 | elmptrab2 | |