![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > df-new | Structured version Visualization version GIF version |
Description: Define the newer than function. This function carries an ordinal to all surreals made on that day. Definition from [Conway] p. 29. (Contributed by Scott Fenton, 17-Dec-2021.) |
Ref | Expression |
---|---|
df-new | ⊢ N = (𝑥 ∈ On ↦ (( M ‘𝑥) ∖ ( O ‘𝑥))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnew 27196 | . 2 class N | |
2 | vx | . . 3 setvar 𝑥 | |
3 | con0 6318 | . . 3 class On | |
4 | 2 | cv 1541 | . . . . 5 class 𝑥 |
5 | cmade 27194 | . . . . 5 class M | |
6 | 4, 5 | cfv 6497 | . . . 4 class ( M ‘𝑥) |
7 | cold 27195 | . . . . 5 class O | |
8 | 4, 7 | cfv 6497 | . . . 4 class ( O ‘𝑥) |
9 | 6, 8 | cdif 3908 | . . 3 class (( M ‘𝑥) ∖ ( O ‘𝑥)) |
10 | 2, 3, 9 | cmpt 5189 | . 2 class (𝑥 ∈ On ↦ (( M ‘𝑥) ∖ ( O ‘𝑥))) |
11 | 1, 10 | wceq 1542 | 1 wff N = (𝑥 ∈ On ↦ (( M ‘𝑥) ∖ ( O ‘𝑥))) |
Colors of variables: wff setvar class |
This definition is referenced by: newval 27207 newf 27210 |
Copyright terms: Public domain | W3C validator |