Description: The image of 0 by the RRHom homomorphism is the ring's zero. (Contributed by Thierry Arnoux, 22-Oct-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | rrh0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zssq | |
|
2 | 0z | |
|
3 | 1 2 | sselii | |
4 | simpl | |
|
5 | simpr | |
|
6 | rrhqima | |
|
7 | 4 5 6 | syl2anc | |
8 | 3 7 | mpan2 | |
9 | rrextdrg | |
|
10 | rrextchr | |
|
11 | eqid | |
|
12 | eqid | |
|
13 | eqid | |
|
14 | 11 12 13 | qqh0 | |
15 | 9 10 14 | syl2anc | |
16 | 8 15 | eqtrd | |