Description: An equivalent formulation of the generalized continuum hypothesis. (Contributed by Mario Carneiro, 15-May-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | gch3 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr | |
|
2 | fvex | |
|
3 | simpl | |
|
4 | 2 3 | eleqtrrid | |
5 | fvex | |
|
6 | 5 3 | eleqtrrid | |
7 | gchaleph2 | |
|
8 | 1 4 6 7 | syl3anc | |
9 | 8 | ralrimiva | |
10 | alephgch | |
|
11 | 10 | ralimi | |
12 | alephfnon | |
|
13 | ffnfv | |
|
14 | 12 13 | mpbiran | |
15 | 11 14 | sylibr | |
16 | 15 | frnd | |
17 | gch2 | |
|
18 | 16 17 | sylibr | |
19 | 9 18 | impbii | |