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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-limits | Structured version Visualization version GIF version |
Description: Define the class of all limit ordinals. (Contributed by Scott Fenton, 11-Apr-2012.) |
Ref | Expression |
---|---|
df-limits | ⊢ Limits = ((On ∩ Fix Bigcup ) ∖ {∅}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | climits 34146 | . 2 class Limits | |
2 | con0 6259 | . . . 4 class On | |
3 | cbigcup 34144 | . . . . 5 class Bigcup | |
4 | 3 | cfix 34145 | . . . 4 class Fix Bigcup |
5 | 2, 4 | cin 3885 | . . 3 class (On ∩ Fix Bigcup ) |
6 | c0 4256 | . . . 4 class ∅ | |
7 | 6 | csn 4561 | . . 3 class {∅} |
8 | 5, 7 | cdif 3883 | . 2 class ((On ∩ Fix Bigcup ) ∖ {∅}) |
9 | 1, 8 | wceq 1539 | 1 wff Limits = ((On ∩ Fix Bigcup ) ∖ {∅}) |
Colors of variables: wff setvar class |
This definition is referenced by: ellimits 34220 limitssson 34221 |
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