Description: Alternate definition of indexed union when B is a set. Definition 15(a) of Suppes p. 44. (Contributed by NM, 27-Jun-1998) (Revised by David Abernethy, 19-Jun-2012)
Ref | Expression | ||
---|---|---|---|
Hypothesis | dfiun2.1 | |- B e. _V |
|
Assertion | dfiun2 | |- U_ x e. A B = U. { y | E. x e. A y = B } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfiun2.1 | |- B e. _V |
|
2 | dfiun2g | |- ( A. x e. A B e. _V -> U_ x e. A B = U. { y | E. x e. A y = B } ) |
|
3 | 1 | a1i | |- ( x e. A -> B e. _V ) |
4 | 2 3 | mprg | |- U_ x e. A B = U. { y | E. x e. A y = B } |