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 ) ) |