Description: A total function is a partial function. (Contributed by Mario Carneiro, 31-Dec-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | fpmg | |- ( ( A e. V /\ B e. W /\ F : A --> B ) -> F e. ( B ^pm A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid | |- A C_ A |
|
2 | elpm2r | |- ( ( ( B e. W /\ A e. V ) /\ ( F : A --> B /\ A C_ A ) ) -> F e. ( B ^pm A ) ) |
|
3 | 1 2 | mpanr2 | |- ( ( ( B e. W /\ A e. V ) /\ F : A --> B ) -> F e. ( B ^pm A ) ) |
4 | 3 | 3impa | |- ( ( B e. W /\ A e. V /\ F : A --> B ) -> F e. ( B ^pm A ) ) |
5 | 4 | 3com12 | |- ( ( A e. V /\ B e. W /\ F : A --> B ) -> F e. ( B ^pm A ) ) |