Description: The axiom of choice implies the ultrafilter lemma. (Contributed by Mario Carneiro, 26-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | acufl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex | ||
2 | 1 | pwex | |
3 | 2 | pwex | |
4 | dfac10 | ||
5 | 4 | biimpi | |
6 | 3 5 | eleqtrrid | |
7 | numufl | ||
8 | 6 7 | syl | |
9 | 1 | a1i | |
10 | 8 9 | 2thd | |
11 | 10 | eqrdv |