Description: The property of being a proper line, generated by two distinct points. (Contributed by Thierry Arnoux, 25-May-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | tglineelsb2.p | |
|
tglineelsb2.i | |
||
tglineelsb2.l | |
||
tglineelsb2.g | |
||
tgelrnln.x | |
||
tgelrnln.y | |
||
tgelrnln.d | |
||
Assertion | tgelrnln | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tglineelsb2.p | |
|
2 | tglineelsb2.i | |
|
3 | tglineelsb2.l | |
|
4 | tglineelsb2.g | |
|
5 | tgelrnln.x | |
|
6 | tgelrnln.y | |
|
7 | tgelrnln.d | |
|
8 | df-ov | |
|
9 | 1 3 2 | tglnfn | |
10 | 4 9 | syl | |
11 | 5 6 | opelxpd | |
12 | df-br | |
|
13 | ideqg | |
|
14 | 12 13 | bitr3id | |
15 | 14 | necon3bbid | |
16 | 15 | biimpar | |
17 | 6 7 16 | syl2anc | |
18 | 11 17 | eldifd | |
19 | fnfvelrn | |
|
20 | 10 18 19 | syl2anc | |
21 | 8 20 | eqeltrid | |