Description: Intersection of two Cartesian products. Exercise 9 of TakeutiZaring p. 25. (Contributed by NM, 3-Aug-1994) (Proof shortened by Andrew Salmon, 27-Aug-2011) Avoid ax-10 , ax-12 . (Revised by SN, 5-May-2025)
Ref | Expression | ||
---|---|---|---|
Assertion | inxp | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relinxp | |
|
2 | relxp | |
|
3 | an4 | |
|
4 | opelxp | |
|
5 | opelxp | |
|
6 | 4 5 | anbi12i | |
7 | elin | |
|
8 | elin | |
|
9 | 7 8 | anbi12i | |
10 | 3 6 9 | 3bitr4i | |
11 | elin | |
|
12 | opelxp | |
|
13 | 10 11 12 | 3bitr4i | |
14 | 1 2 13 | eqrelriiv | |