Description: Lemma for dath . Rotate triangles Y = P Q R and Z = S T U to allow reuse of analogous proofs. (Contributed by NM, 19-Aug-2012)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dalema.ph | |
|
dalemc.l | |
||
dalemc.j | |
||
dalemc.a | |
||
dalemrot.y | |
||
dalemrot.z | |
||
Assertion | dalemrotyz | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dalema.ph | |
|
2 | dalemc.l | |
|
3 | dalemc.j | |
|
4 | dalemc.a | |
|
5 | dalemrot.y | |
|
6 | dalemrot.z | |
|
7 | simpr | |
|
8 | 1 3 4 | dalemqrprot | |
9 | 5 8 | eqtr4id | |
10 | 9 | adantr | |
11 | 1 | dalemkehl | |
12 | 1 | dalemtea | |
13 | 1 | dalemuea | |
14 | 1 | dalemsea | |
15 | 3 4 | hlatjrot | |
16 | 11 12 13 14 15 | syl13anc | |
17 | 6 16 | eqtr4id | |
18 | 17 | adantr | |
19 | 7 10 18 | 3eqtr3d | |