Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012)
Ref | Expression | ||
---|---|---|---|
Hypotheses | preq1i.1 | |- A = B |
|
preq12i.2 | |- C = D |
||
Assertion | preq12i | |- { A , C } = { B , D } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1i.1 | |- A = B |
|
2 | preq12i.2 | |- C = D |
|
3 | preq12 | |- ( ( A = B /\ C = D ) -> { A , C } = { B , D } ) |
|
4 | 1 2 3 | mp2an | |- { A , C } = { B , D } |