Description: A basic open set in the product topology. (Contributed by Mario Carneiro, 3-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ptbas.1 | |
|
Assertion | elptr | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ptbas.1 | |
|
2 | simp2l | |
|
3 | simp1 | |
|
4 | 2 3 | fnexd | |
5 | simp2r | |
|
6 | difeq2 | |
|
7 | 6 | raleqdv | |
8 | 7 | rspcev | |
9 | 8 | 3ad2ant3 | |
10 | 2 5 9 | 3jca | |
11 | fveq1 | |
|
12 | 11 | eqcomd | |
13 | 12 | ixpeq2dv | |
14 | 13 | biantrud | |
15 | fneq1 | |
|
16 | 11 | eleq1d | |
17 | 16 | ralbidv | |
18 | 11 | eqeq1d | |
19 | 18 | rexralbidv | |
20 | 15 17 19 | 3anbi123d | |
21 | 14 20 | bitr3d | |
22 | 4 10 21 | spcedv | |
23 | 1 | elpt | |
24 | 22 23 | sylibr | |