Description: Different elements have different preimages. (Contributed by Thierry Arnoux, 7-May-2023)
Ref | Expression | ||
---|---|---|---|
Hypotheses | preimane.f | |
|
preimane.x | |
||
preimane.y | |
||
preimane.1 | |
||
Assertion | preimane | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preimane.f | |
|
2 | preimane.x | |
|
3 | preimane.y | |
|
4 | preimane.1 | |
|
5 | sneqrg | |
|
6 | 3 5 | syl | |
7 | 6 | necon3d | |
8 | 2 7 | mpd | |
9 | funimacnv | |
|
10 | 1 9 | syl | |
11 | 3 | snssd | |
12 | df-ss | |
|
13 | 11 12 | sylib | |
14 | 10 13 | eqtrd | |
15 | funimacnv | |
|
16 | 1 15 | syl | |
17 | 4 | snssd | |
18 | df-ss | |
|
19 | 17 18 | sylib | |
20 | 16 19 | eqtrd | |
21 | 8 14 20 | 3netr4d | |
22 | imaeq2 | |
|
23 | 22 | necon3i | |
24 | 21 23 | syl | |