Definition df-singleton 31138

Description: Define the singleton function. See brsingle 31194 for its value. (Contributed by Scott Fenton, 4-Apr-2014.)

Assertion

Ref	Expression
df-singleton	⊢ Singleton = ((V × V) ∖ ran ((V ⊗ E ) △ ( I ⊗ V)))

Detailed syntax breakdown of Definition df-singleton

Step	Hyp	Ref	Expression
1		csingle 31114	. 2 class Singleton
2		cvv 3173	. . . 4 class V
3	2, 2	cxp 5036	. . 3 class (V × V)
4		cep 4947	. . . . . 6 class E
5	2, 4	ctxp 31106	. . . . 5 class (V ⊗ E )
6		cid 4948	. . . . . 6 class I
7	6, 2	ctxp 31106	. . . . 5 class ( I ⊗ V)
8	5, 7	csymdif 3805	. . . 4 class ((V ⊗ E ) △ ( I ⊗ V))
9	8	crn 5039	. . 3 class ran ((V ⊗ E ) △ ( I ⊗ V))
10	3, 9	cdif 3537	. 2 class ((V × V) ∖ ran ((V ⊗ E ) △ ( I ⊗ V)))
11	1, 10	wceq 1475	1 wff Singleton = ((V × V) ∖ ran ((V ⊗ E ) △ ( I ⊗ V)))

This definition is referenced by:  brsingle  31194  fnsingle  31196