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 X. _V ) \ ran ( ( _V (x) _E ) /_\ ( ( _E o. _E ) (x) _V ) ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cbigcup 
 |-  Bigcup
1 cvv 
 |-  _V
2 1 1 cxp 
 |-  ( _V X. _V )
3 cep 
 |-  _E
4 1 3 ctxp 
 |-  ( _V (x) _E )
5 3 3 ccom 
 |-  ( _E o. _E )
6 5 1 ctxp 
 |-  ( ( _E o. _E ) (x) _V )
7 4 6 csymdif 
 |-  ( ( _V (x) _E ) /_\ ( ( _E o. _E ) (x) _V ) )
8 7 crn 
 |-  ran ( ( _V (x) _E ) /_\ ( ( _E o. _E ) (x) _V ) )
9 2 8 cdif 
 |-  ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( ( _E o. _E ) (x) _V ) ) )
10 0 9 wceq 
 |-  Bigcup = ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( ( _E o. _E ) (x) _V ) ) )