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Mirrors > Home > ILE Home > Th. List > repizf2lem | Unicode version |
Description: Lemma for repizf2 3936. If we have a function-like proposition which provides at most one value of for each in a set , we can change "at most one" to "exactly one" by restricting the values of to those values for which the proposition provides a value of . (Contributed by Jim Kingdon, 7-Sep-2018.) |
Ref | Expression |
---|---|
repizf2lem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mo 1945 | . . . 4 | |
2 | 1 | imbi2i 224 | . . 3 |
3 | 2 | albii 1399 | . 2 |
4 | df-ral 2353 | . 2 | |
5 | df-ral 2353 | . . 3 | |
6 | rabid 2529 | . . . . . 6 | |
7 | 6 | imbi1i 236 | . . . . 5 |
8 | impexp 259 | . . . . 5 | |
9 | 7, 8 | bitri 182 | . . . 4 |
10 | 9 | albii 1399 | . . 3 |
11 | 5, 10 | bitri 182 | . 2 |
12 | 3, 4, 11 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wex 1421 wcel 1433 weu 1941 wmo 1942 wral 2348 crab 2352 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-sb 1686 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-ral 2353 df-rab 2357 |
This theorem is referenced by: repizf2 3936 |
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