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Mirrors > Home > MPE Home > Th. List > df-subs | Structured version Visualization version GIF version |
Description: Define surreal subtraction. (Contributed by Scott Fenton, 20-Aug-2024.) |
Ref | Expression |
---|---|
df-subs | ⊢ -s = (𝑥 ∈ No , 𝑦 ∈ No ↦ (𝑥 +s ( -us ‘𝑦))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csubs 27322 | . 2 class -s | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . 3 setvar 𝑦 | |
4 | csur 26991 | . . 3 class No | |
5 | 2 | cv 1541 | . . . 4 class 𝑥 |
6 | 3 | cv 1541 | . . . . 5 class 𝑦 |
7 | cnegs 27321 | . . . . 5 class -us | |
8 | 6, 7 | cfv 6497 | . . . 4 class ( -us ‘𝑦) |
9 | cadds 27274 | . . . 4 class +s | |
10 | 5, 8, 9 | co 7358 | . . 3 class (𝑥 +s ( -us ‘𝑦)) |
11 | 2, 3, 4, 4, 10 | cmpo 7360 | . 2 class (𝑥 ∈ No , 𝑦 ∈ No ↦ (𝑥 +s ( -us ‘𝑦))) |
12 | 1, 11 | wceq 1542 | 1 wff -s = (𝑥 ∈ No , 𝑦 ∈ No ↦ (𝑥 +s ( -us ‘𝑦))) |
Colors of variables: wff setvar class |
This definition is referenced by: subsfn 27326 subsval 27354 |
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