Description: Existence of a restriction of the function operation map. (Contributed by NM, 20-Oct-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ofmresex.a | |- ( ph -> A e. V ) |
|
ofmresex.b | |- ( ph -> B e. W ) |
||
Assertion | ofmresex | |- ( ph -> ( oF R |` ( A X. B ) ) e. _V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ofmresex.a | |- ( ph -> A e. V ) |
|
2 | ofmresex.b | |- ( ph -> B e. W ) |
|
3 | 1 2 | xpexd | |- ( ph -> ( A X. B ) e. _V ) |
4 | ofexg | |- ( ( A X. B ) e. _V -> ( oF R |` ( A X. B ) ) e. _V ) |
|
5 | 3 4 | syl | |- ( ph -> ( oF R |` ( A X. B ) ) e. _V ) |