Description: The composition of two sets is a set. (Contributed by SN, 7-Feb-2025)
Ref | Expression | ||
---|---|---|---|
Hypotheses | coexd.1 | |- ( ph -> A e. V ) |
|
coexd.2 | |- ( ph -> B e. W ) |
||
Assertion | coexd | |- ( ph -> ( A o. B ) e. _V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coexd.1 | |- ( ph -> A e. V ) |
|
2 | coexd.2 | |- ( ph -> B e. W ) |
|
3 | coexg | |- ( ( A e. V /\ B e. W ) -> ( A o. B ) e. _V ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( A o. B ) e. _V ) |