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Mirrors > Home > MPE Home > Th. List > df-gch | Structured version Visualization version Unicode version |
Description: Define the collection of "GCH-sets", or sets for which the generalized continuum hypothesis holds. In this language the generalized continuum hypothesis can be expressed as GCH . A set satisfies the generalized continuum hypothesis if it is finite or there is no set strictly between and its powerset in cardinality. The continuum hypothesis is equivalent to GCH. (Contributed by Mario Carneiro, 15-May-2015.) |
Ref | Expression |
---|---|
df-gch | GCH |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cgch 9442 | . 2 GCH | |
2 | cfn 7955 | . . 3 | |
3 | vx | . . . . . . . . 9 | |
4 | 3 | cv 1482 | . . . . . . . 8 |
5 | vy | . . . . . . . . 9 | |
6 | 5 | cv 1482 | . . . . . . . 8 |
7 | csdm 7954 | . . . . . . . 8 | |
8 | 4, 6, 7 | wbr 4653 | . . . . . . 7 |
9 | 4 | cpw 4158 | . . . . . . . 8 |
10 | 6, 9, 7 | wbr 4653 | . . . . . . 7 |
11 | 8, 10 | wa 384 | . . . . . 6 |
12 | 11 | wn 3 | . . . . 5 |
13 | 12, 5 | wal 1481 | . . . 4 |
14 | 13, 3 | cab 2608 | . . 3 |
15 | 2, 14 | cun 3572 | . 2 |
16 | 1, 15 | wceq 1483 | 1 GCH |
Colors of variables: wff setvar class |
This definition is referenced by: elgch 9444 fingch 9445 |
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