Description: Two things in a binary relation belong to the relation's domain. (Contributed by NM, 17-May-1996) (Revised by Mario Carneiro, 26-Apr-2015)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | brel.1 | |- R C_ ( C X. D ) |
|
| Assertion | brel | |- ( A R B -> ( A e. C /\ B e. D ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | brel.1 | |- R C_ ( C X. D ) |
|
| 2 | 1 | ssbri | |- ( A R B -> A ( C X. D ) B ) |
| 3 | brxp | |- ( A ( C X. D ) B <-> ( A e. C /\ B e. D ) ) |
|
| 4 | 2 3 | sylib | |- ( A R B -> ( A e. C /\ B e. D ) ) |