Description: An infinite GCH-set is Dedekind-infinite. (Contributed by Mario Carneiro, 31-May-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | gchinf | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gchdju1 | |
|
2 | 1 | ensymd | |
3 | isfin4-2 | |
|
4 | 3 | adantr | |
5 | isfin4p1 | |
|
6 | sdomnen | |
|
7 | 5 6 | sylbi | |
8 | 4 7 | syl6bir | |
9 | 2 8 | mt4d | |