Description: Equality of two unordered pairs when one member of each pair contains the other member. (Contributed by NM, 16-Oct-1996) (Revised by AV, 15-Jun-2022)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | preleq.b | |- B e. _V |
|
| Assertion | preleq | |- ( ( ( A e. B /\ C e. D ) /\ { A , B } = { C , D } ) -> ( A = C /\ B = D ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | preleq.b | |- B e. _V |
|
| 2 | preleqg | |- ( ( ( A e. B /\ B e. _V /\ C e. D ) /\ { A , B } = { C , D } ) -> ( A = C /\ B = D ) ) |
|
| 3 | 1 2 | mp3anl2 | |- ( ( ( A e. B /\ C e. D ) /\ { A , B } = { C , D } ) -> ( A = C /\ B = D ) ) |