Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-bigcup Structured version   Visualization version   GIF version

Definition df-bigcup 31134
 Description: Define the Bigcup function, which, per fvbigcup 31179, 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
StepHypRef Expression
1 cbigcup 31110 . 2 class Bigcup
2 cvv 3173 . . . 4 class V
32, 2cxp 5036 . . 3 class (V × V)
4 cep 4947 . . . . . 6 class E
52, 4ctxp 31106 . . . . 5 class (V ⊗ E )
64, 4ccom 5042 . . . . . 6 class ( E ∘ E )
76, 2ctxp 31106 . . . . 5 class (( E ∘ E ) ⊗ V)
85, 7csymdif 3805 . . . 4 class ((V ⊗ E ) △ (( E ∘ E ) ⊗ V))
98crn 5039 . . 3 class ran ((V ⊗ E ) △ (( E ∘ E ) ⊗ V))
103, 9cdif 3537 . 2 class ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ E ) ⊗ V)))
111, 10wceq 1475 1 wff Bigcup = ((V × V) ∖ ran ((V ⊗ E ) △ (( E ∘ E ) ⊗ V)))
 Colors of variables: wff setvar class This definition is referenced by:  relbigcup  31174  brbigcup  31175
 Copyright terms: Public domain W3C validator