Description: Lemma for structure products. (Contributed by Mario Carneiro, 3-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | prdsbasex.b | |- B = X_ x e. dom R ( Base ` ( R ` x ) ) |
|
Assertion | prdsbasex | |- B e. _V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prdsbasex.b | |- B = X_ x e. dom R ( Base ` ( R ` x ) ) |
|
2 | ixpexg | |- ( A. x e. dom R ( Base ` ( R ` x ) ) e. _V -> X_ x e. dom R ( Base ` ( R ` x ) ) e. _V ) |
|
3 | fvexd | |- ( x e. dom R -> ( Base ` ( R ` x ) ) e. _V ) |
|
4 | 2 3 | mprg | |- X_ x e. dom R ( Base ` ( R ` x ) ) e. _V |
5 | 1 4 | eqeltri | |- B e. _V |