Description: Express injection for a mapping operation. (Contributed by Mario Carneiro, 2-Jan-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | f1mpt.1 | |
|
f1mpt.2 | |
||
Assertion | f1mpt | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1mpt.1 | |
|
2 | f1mpt.2 | |
|
3 | nfmpt1 | |
|
4 | 1 3 | nfcxfr | |
5 | nfcv | |
|
6 | 4 5 | dff13f | |
7 | 1 | fmpt | |
8 | 7 | anbi1i | |
9 | 2 | eleq1d | |
10 | 9 | cbvralvw | |
11 | raaanv | |
|
12 | 1 | fvmpt2 | |
13 | 2 1 | fvmptg | |
14 | 12 13 | eqeqan12d | |
15 | 14 | an4s | |
16 | 15 | imbi1d | |
17 | 16 | ex | |
18 | 17 | ralimdva | |
19 | ralbi | |
|
20 | 18 19 | syl6 | |
21 | 20 | ralimia | |
22 | ralbi | |
|
23 | 21 22 | syl | |
24 | 11 23 | sylbir | |
25 | 10 24 | sylan2b | |
26 | 25 | anidms | |
27 | 26 | pm5.32i | |
28 | 6 8 27 | 3bitr2i | |