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Metamath Proof Explorer
Description: Define the class of all limit ordinals. (Contributed by Scott Fenton, 11-Apr-2012)
|
|
Ref |
Expression |
|
Assertion |
df-limits |
⊢ Limits = ( ( On ∩ Fix Bigcup ) ∖ { ∅ } ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
climits |
⊢ Limits |
| 1 |
|
con0 |
⊢ On |
| 2 |
|
cbigcup |
⊢ Bigcup |
| 3 |
2
|
cfix |
⊢ Fix Bigcup |
| 4 |
1 3
|
cin |
⊢ ( On ∩ Fix Bigcup ) |
| 5 |
|
c0 |
⊢ ∅ |
| 6 |
5
|
csn |
⊢ { ∅ } |
| 7 |
4 6
|
cdif |
⊢ ( ( On ∩ Fix Bigcup ) ∖ { ∅ } ) |
| 8 |
0 7
|
wceq |
⊢ Limits = ( ( On ∩ Fix Bigcup ) ∖ { ∅ } ) |