Description: The "opposite to a line" relation is irreflexive. (Contributed by Thierry Arnoux, 4-Mar-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hpg.p | |
|
hpg.d | |
||
hpg.i | |
||
hpg.o | |
||
opphl.l | |
||
opphl.d | |
||
opphl.g | |
||
oppnid.1 | |
||
Assertion | oppnid | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hpg.p | |
|
2 | hpg.d | |
|
3 | hpg.i | |
|
4 | hpg.o | |
|
5 | opphl.l | |
|
6 | opphl.d | |
|
7 | opphl.g | |
|
8 | oppnid.1 | |
|
9 | 7 | ad3antrrr | |
10 | 8 | ad3antrrr | |
11 | 6 | ad3antrrr | |
12 | simplr | |
|
13 | 1 5 3 9 11 12 | tglnpt | |
14 | simpr | |
|
15 | 1 2 3 9 10 13 14 | axtgbtwnid | |
16 | 15 12 | eqeltrd | |
17 | 1 2 3 4 8 8 | islnopp | |
18 | 17 | simplbda | |
19 | 16 18 | r19.29a | |
20 | 17 | simprbda | |
21 | 20 | simpld | |
22 | 19 21 | pm2.65da | |