Description: Biconditional equality lemma for unordered pairs, deduction form. Two unordered pairs have the same first element iff the second elements are equal. (Contributed by AV, 18-Dec-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | preq1b.a | |
|
preq1b.b | |
||
Assertion | preq2b | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1b.a | |
|
2 | preq1b.b | |
|
3 | prcom | |
|
4 | prcom | |
|
5 | 3 4 | eqeq12i | |
6 | 1 2 | preq1b | |
7 | 5 6 | bitrid | |