Metamath Proof Explorer


Definition df-bigcup

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

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

Detailed syntax breakdown

Step Hyp Ref Expression
0 cbigcup Bigcup
1 cvv V
2 1 1 cxp ( V × V )
3 cep E
4 1 3 ctxp ( V ⊗ E )
5 3 3 ccom ( E ∘ E )
6 5 1 ctxp ( ( E ∘ E ) ⊗ V )
7 4 6 csymdif ( ( V ⊗ E ) △ ( ( E ∘ E ) ⊗ V ) )
8 7 crn ran ( ( V ⊗ E ) △ ( ( E ∘ E ) ⊗ V ) )
9 2 8 cdif ( ( V × V ) ∖ ran ( ( V ⊗ E ) △ ( ( E ∘ E ) ⊗ V ) ) )
10 0 9 wceq Bigcup = ( ( V × V ) ∖ ran ( ( V ⊗ E ) △ ( ( E ∘ E ) ⊗ V ) ) )