Description: The Cartesian product with the empty set is empty. Part of Theorem 3.13(ii) of Monk1 p. 37. (Contributed by NM, 4-Jul-1994)
Ref | Expression | ||
---|---|---|---|
Assertion | 0xp | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel | |
|
2 | simprl | |
|
3 | 1 2 | mto | |
4 | 3 | nex | |
5 | 4 | nex | |
6 | elxp | |
|
7 | 5 6 | mtbir | |
8 | 7 | nel0 | |