Definition df-old 34032

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.)

Assertion

Ref	Expression
df-old	⊢ O = (𝑥 ∈ On ↦ ∪ ( M “ 𝑥))

Detailed syntax breakdown of Definition df-old

Step	Hyp	Ref	Expression
1		cold 34027	. 2 class O
2		vx	. . 3 setvar 𝑥
3		con0 6266	. . 3 class On
4		cmade 34026	. . . . 5 class M
5	2	cv 1538	. . . . 5 class 𝑥
6	4, 5	cima 5592	. . . 4 class ( M “ 𝑥)
7	6	cuni 4839	. . 3 class ∪ ( M “ 𝑥)
8	2, 3, 7	cmpt 5157	. 2 class (𝑥 ∈ On ↦ ∪ ( M “ 𝑥))
9	1, 8	wceq 1539	1 wff O = (𝑥 ∈ On ↦ ∪ ( M “ 𝑥))

This definition is referenced by:  oldval  34038  oldf  34041