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Definition df-omul 5945
Description: Define the ordinal multiplication operation. (Contributed by NM, 26-Aug-1995.)
Assertion
Ref Expression
df-omul ·𝑜 = (x On, y On ↦ (rec((z V ↦ (z +𝑜 x)), ∅)‘y))
Distinct variable group:   x,y,z

Detailed syntax breakdown of Definition df-omul
StepHypRef Expression
1 comu 5938 . 2 class ·𝑜
2 vx . . 3 setvar x
3 vy . . 3 setvar y
4 con0 4066 . . 3 class On
53cv 1241 . . . 4 class y
6 vz . . . . . 6 setvar z
7 cvv 2551 . . . . . 6 class V
86cv 1241 . . . . . . 7 class z
92cv 1241 . . . . . . 7 class x
10 coa 5937 . . . . . . 7 class +𝑜
118, 9, 10co 5455 . . . . . 6 class (z +𝑜 x)
126, 7, 11cmpt 3809 . . . . 5 class (z V ↦ (z +𝑜 x))
13 c0 3218 . . . . 5 class
1412, 13crdg 5896 . . . 4 class rec((z V ↦ (z +𝑜 x)), ∅)
155, 14cfv 4845 . . 3 class (rec((z V ↦ (z +𝑜 x)), ∅)‘y)
162, 3, 4, 4, 15cmpt2 5457 . 2 class (x On, y On ↦ (rec((z V ↦ (z +𝑜 x)), ∅)‘y))
171, 16wceq 1242 1 wff ·𝑜 = (x On, y On ↦ (rec((z V ↦ (z +𝑜 x)), ∅)‘y))
Colors of variables: wff set class
This definition is referenced by:  fnom  5969  omexg  5970  omv  5974
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