Definition df-bigcup 33744

Description: Define the Bigcup function, which, per fvbigcup 33788, carries a set to its union. (Contributed by Scott Fenton, 11-Apr-2012.)

Assertion

Ref	Expression
df-bigcup	⊢ Bigcup = ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ E ) ⊗ V)))

Detailed syntax breakdown of Definition df-bigcup

Step	Hyp	Ref	Expression
1		cbigcup 33720	. 2 class Bigcup
2		cvv 3409	. . . 4 class V
3	2, 2	cxp 5526	. . 3 class (V × V)
4		cep 5438	. . . . . 6 class E
5	2, 4	ctxp 33716	. . . . 5 class (V ⊗ E )
6	4, 4	ccom 5532	. . . . . 6 class ( E ∘ E )
7	6, 2	ctxp 33716	. . . . 5 class (( E ∘ E ) ⊗ V)
8	5, 7	csymdif 4148	. . . 4 class ((V ⊗ E ) △ (( E ∘ E ) ⊗ V))
9	8	crn 5529	. . 3 class ran ((V ⊗ E ) △ (( E ∘ E ) ⊗ V))
10	3, 9	cdif 3857	. 2 class ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ E ) ⊗ V)))
11	1, 10	wceq 1538	1 wff Bigcup = ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ E ) ⊗ V)))

This definition is referenced by:  relbigcup  33783  brbigcup  33784