Description: Deduction about composition of classes with no relational content in common. (Contributed by RP, 24-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypothesis | coemptyd.1 | |- ( ph -> ( dom A i^i ran B ) = (/) ) |
|
Assertion | coemptyd | |- ( ph -> ( A o. B ) = (/) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coemptyd.1 | |- ( ph -> ( dom A i^i ran B ) = (/) ) |
|
2 | coeq0 | |- ( ( A o. B ) = (/) <-> ( dom A i^i ran B ) = (/) ) |
|
3 | 1 2 | sylibr | |- ( ph -> ( A o. B ) = (/) ) |