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Definition df-made 32236
Description: Define the made by function. This function carries an ordinal to all surreals made by sections of surreals older than it. (Contributed by Scott Fenton, 17-Dec-2021.)
Assertion
Ref Expression
df-made M = recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ran 𝑓 × 𝒫 ran 𝑓))))

Detailed syntax breakdown of Definition df-made
StepHypRef Expression
1 cmade 32231 . 2 class M
2 vf . . . 4 setvar 𝑓
3 cvv 3340 . . . 4 class V
4 cscut 32204 . . . . 5 class |s
52cv 1631 . . . . . . . . 9 class 𝑓
65crn 5267 . . . . . . . 8 class ran 𝑓
76cuni 4588 . . . . . . 7 class ran 𝑓
87cpw 4302 . . . . . 6 class 𝒫 ran 𝑓
98, 8cxp 5264 . . . . 5 class (𝒫 ran 𝑓 × 𝒫 ran 𝑓)
104, 9cima 5269 . . . 4 class ( |s “ (𝒫 ran 𝑓 × 𝒫 ran 𝑓))
112, 3, 10cmpt 4881 . . 3 class (𝑓 ∈ V ↦ ( |s “ (𝒫 ran 𝑓 × 𝒫 ran 𝑓)))
1211crecs 7636 . 2 class recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ran 𝑓 × 𝒫 ran 𝑓))))
131, 12wceq 1632 1 wff M = recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ran 𝑓 × 𝒫 ran 𝑓))))
Colors of variables: wff setvar class
This definition is referenced by:  madeval  32241
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