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Mirrors > Home > ILE Home > Th. List > repizf2lem | Unicode version |
Description: Lemma for repizf2 4135. 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 2017 | . . . 4 | |
2 | 1 | imbi2i 225 | . . 3 |
3 | 2 | albii 1457 | . 2 |
4 | df-ral 2447 | . 2 | |
5 | df-ral 2447 | . . 3 | |
6 | rabid 2639 | . . . . . 6 | |
7 | 6 | imbi1i 237 | . . . . 5 |
8 | impexp 261 | . . . . 5 | |
9 | 7, 8 | bitri 183 | . . . 4 |
10 | 9 | albii 1457 | . . 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 1340 wex 1479 weu 2013 wmo 2014 wcel 2135 wral 2442 crab 2446 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-sb 1750 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-ral 2447 df-rab 2451 |
This theorem is referenced by: repizf2 4135 |
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