Definition df-succf 36072

Description: Define the successor function. See its alternate version dfsuccf2 36143. See brsuccf 36142 for its value. Cf. the equivalent df-sucmap 38801 family. (Contributed by Scott Fenton, 14-Apr-2014.)

Assertion

Ref	Expression
df-succf	⊢ Succ = (Cup ∘ ( I ⊗ Singleton))

Detailed syntax breakdown of Definition df-succf

Step	Hyp	Ref	Expression
1		csuccf 36048	. 2 class Succ
2		ccup 36046	. . 3 class Cup
3		cid 5520	. . . 4 class I
4		csingle 36038	. . . 4 class Singleton
5	3, 4	ctxp 36030	. . 3 class ( I ⊗ Singleton)
6	2, 5	ccom 5630	. 2 class (Cup ∘ ( I ⊗ Singleton))
7	1, 6	wceq 1542	1 wff Succ = (Cup ∘ ( I ⊗ Singleton))

This definition is referenced by:  brsuccf  36142  dfsuccf2  36143