Definition df-succl 39159

Description: Define Suc as the class of all successors, i.e. the range of the successor map: 𝑛 ∈ Suc iff ∃𝑚suc 𝑚 = 𝑛 (see dfsuccl2 39160). By injectivity of suc (suc11reg 9598), every 𝑛 ∈ Suc has at most one predecessor, which is exactly what pre 𝑛 (df-pre 39165) names. Cf. dfsuccl3 39163 and dfsuccl4 39164. (Contributed by Peter Mazsa, 25-Jan-2026.)

Assertion

Ref	Expression
df-succl	⊢ Suc = ran SucMap

Detailed syntax breakdown of Definition df-succl

Step	Hyp	Ref	Expression
1		csuccl 38869	. 2 class Suc
2		csucmap 38868	. . 3 class SucMap
3	2	crn 5667	. 2 class ran SucMap
4	1, 3	wceq 1570	1 wff Suc = ran SucMap

This definition is used by:  dfsuccl2  39160  eupre  39184  sucpre  39187  presuc  39188