Description: Two ways of saying a relation is symmetric. (Contributed by FL, 31-Aug-2009)
Ref | Expression | ||
---|---|---|---|
Assertion | relcnveq3 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqss | |
|
2 | cnvsym | |
|
3 | 2 | biimpi | |
4 | 3 | a1d | |
5 | 4 | adantl | |
6 | 5 | com12 | |
7 | dfrel2 | |
|
8 | cnvss | |
|
9 | sseq1 | |
|
10 | 8 9 | syl5ibcom | |
11 | 2 10 | sylbir | |
12 | 11 | com12 | |
13 | 7 12 | sylbi | |
14 | 2 | biimpri | |
15 | 13 14 | jca2 | |
16 | 6 15 | impbid | |
17 | 1 16 | bitrid | |