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Mirrors > Home > HOLE Home > Th. List > ax-inf | Unicode version |
Description: The axiom of infinity:
the set of "individuals" is not Dedekind-finite.
Using the axiom of choice, we can show that this is equivalent to an
embedding of the natural numbers in ![]() |
Ref | Expression |
---|---|
ax-inf |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | kt 8 |
. 2
term ![]() | |
2 | tex 123 |
. . 3
term ![]() | |
3 | hi 4 |
. . . . 5
type ![]() | |
4 | 3, 3 | ht 2 |
. . . 4
type ![]() ![]() ![]() ![]() ![]() |
5 | vf |
. . . 4
var ![]() | |
6 | tf11 189 | . . . . . 6 term 1-1 | |
7 | 4, 5 | tv 1 |
. . . . . 6
term ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 6, 7 | kc 5 |
. . . . 5
term ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | tne 120 |
. . . . . 6
term ![]() | |
10 | tfo 190 | . . . . . . 7 term onto | |
11 | 10, 7 | kc 5 |
. . . . . 6
term ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 9, 11 | kc 5 |
. . . . 5
term ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | tan 119 |
. . . . 5
term ![]() | |
14 | 8, 12, 13 | kbr 9 |
. . . 4
term ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 4, 5, 14 | kl 6 |
. . 3
term ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 2, 15 | kc 5 |
. 2
term ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 1, 16 | wffMMJ2 11 |
1
wff ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: type var term |
This axiom is referenced by: (None) |
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