Description: Show inverse for the "swap components" operation on a Cartesian product. (Contributed by Mario Carneiro, 21-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | txswaphmeolem | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id | |
|
2 | 1 | mpompt | |
3 | mptresid | |
|
4 | opelxpi | |
|
5 | 4 | ancoms | |
6 | 5 | adantl | |
7 | eqidd | |
|
8 | sneq | |
|
9 | 8 | cnveqd | |
10 | 9 | unieqd | |
11 | opswap | |
|
12 | 10 11 | eqtrdi | |
13 | 12 | mpompt | |
14 | 13 | eqcomi | |
15 | 14 | a1i | |
16 | 6 7 15 12 | fmpoco | |
17 | 16 | mptru | |
18 | 2 3 17 | 3eqtr4ri | |