Description: The union of two finite sets is finite. (Contributed by Glauco Siliprandi, 5-Feb-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | unfid.1 | |- ( ph -> A e. Fin ) |
|
unfid.2 | |- ( ph -> B e. Fin ) |
||
Assertion | unfid | |- ( ph -> ( A u. B ) e. Fin ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unfid.1 | |- ( ph -> A e. Fin ) |
|
2 | unfid.2 | |- ( ph -> B e. Fin ) |
|
3 | unfi | |- ( ( A e. Fin /\ B e. Fin ) -> ( A u. B ) e. Fin ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( A u. B ) e. Fin ) |