Description: A set of size two is a proper unordered pair. (Contributed by AV, 1-Nov-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | hash2prb | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hash2exprb | |
|
2 | vex | |
|
3 | 2 | prid1 | |
4 | vex | |
|
5 | 4 | prid2 | |
6 | 3 5 | pm3.2i | |
7 | eleq2 | |
|
8 | eleq2 | |
|
9 | 7 8 | anbi12d | |
10 | 6 9 | mpbiri | |
11 | 10 | adantl | |
12 | 11 | pm4.71ri | |
13 | 12 | 2exbii | |
14 | 13 | a1i | |
15 | r2ex | |
|
16 | 15 | bicomi | |
17 | 16 | a1i | |
18 | 1 14 17 | 3bitrd | |