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Metamath Proof Explorer

Definition df-succf

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

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

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		csuccf	⊢ Succ
1		ccup	⊢ Cup
2		cid	⊢ I
3		csingle	⊢ Singleton
4	2 3	ctxp	⊢ ( I ⊗ Singleton )
5	1 4	ccom	⊢ ( Cup ∘ ( I ⊗ Singleton ) )
6	0 5	wceq	⊢ Succ = ( Cup ∘ ( I ⊗ Singleton ) )