Description: The union of two functions with disjoint domains, a deduction version. (Contributed by metakunt, 28-May-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | fnund.1 | |- ( ph -> F Fn A ) |
|
fnund.2 | |- ( ph -> G Fn B ) |
||
fnund.3 | |- ( ph -> ( A i^i B ) = (/) ) |
||
Assertion | fnund | |- ( ph -> ( F u. G ) Fn ( A u. B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnund.1 | |- ( ph -> F Fn A ) |
|
2 | fnund.2 | |- ( ph -> G Fn B ) |
|
3 | fnund.3 | |- ( ph -> ( A i^i B ) = (/) ) |
|
4 | fnun | |- ( ( ( F Fn A /\ G Fn B ) /\ ( A i^i B ) = (/) ) -> ( F u. G ) Fn ( A u. B ) ) |
|
5 | 1 2 3 4 | syl21anc | |- ( ph -> ( F u. G ) Fn ( A u. B ) ) |