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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-old | Structured version Visualization version GIF version |
Description: Define the older than function. This function carries an ordinal to all surreals made by a previous ordinal. Definition from [Conway] p. 29. (Contributed by Scott Fenton, 17-Dec-2021.) |
Ref | Expression |
---|---|
df-old | ⊢ O = (𝑥 ∈ On ↦ ∪ ( M “ 𝑥)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cold 33668 | . 2 class O | |
2 | vx | . . 3 setvar 𝑥 | |
3 | con0 6172 | . . 3 class On | |
4 | cmade 33667 | . . . . 5 class M | |
5 | 2 | cv 1541 | . . . . 5 class 𝑥 |
6 | 4, 5 | cima 5528 | . . . 4 class ( M “ 𝑥) |
7 | 6 | cuni 4796 | . . 3 class ∪ ( M “ 𝑥) |
8 | 2, 3, 7 | cmpt 5110 | . 2 class (𝑥 ∈ On ↦ ∪ ( M “ 𝑥)) |
9 | 1, 8 | wceq 1542 | 1 wff O = (𝑥 ∈ On ↦ ∪ ( M “ 𝑥)) |
Colors of variables: wff setvar class |
This definition is referenced by: oldval 33679 oldf 33682 |
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