Description: The domain of a Cartesian product is included in its first factor. (Contributed by NM, 19-Mar-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | dmxpss | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpeq2 | |
|
2 | xp0 | |
|
3 | 1 2 | eqtrdi | |
4 | 3 | dmeqd | |
5 | dm0 | |
|
6 | 4 5 | eqtrdi | |
7 | 0ss | |
|
8 | 6 7 | eqsstrdi | |
9 | dmxp | |
|
10 | eqimss | |
|
11 | 9 10 | syl | |
12 | 8 11 | pm2.61ine | |