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Mirrors > Home > ILE Home > Th. List > repizf2lem | Unicode version |
Description: Lemma for repizf2 4081. 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 2001 | . . . 4 | |
2 | 1 | imbi2i 225 | . . 3 |
3 | 2 | albii 1446 | . 2 |
4 | df-ral 2419 | . 2 | |
5 | df-ral 2419 | . . 3 | |
6 | rabid 2604 | . . . . . 6 | |
7 | 6 | imbi1i 237 | . . . . 5 |
8 | impexp 261 | . . . . 5 | |
9 | 7, 8 | bitri 183 | . . . 4 |
10 | 9 | albii 1446 | . . 3 |
11 | 5, 10 | bitri 183 | . 2 |
12 | 3, 4, 11 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wex 1468 wcel 1480 weu 1997 wmo 1998 wral 2414 crab 2418 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-ral 2419 df-rab 2423 |
This theorem is referenced by: repizf2 4081 |
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