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Mirrors > Home > ILE Home > Th. List > repizf2 | Unicode version |
Description: Replacement. This version of replacement is stronger than repizf 4105 in the sense that does not need to map all values of in to a value of . The resulting set contains those elements for which there is a value of and in that sense, this theorem combines repizf 4105 with ax-sep 4107. Another variation would be but we don't have a proof of that yet. (Contributed by Jim Kingdon, 7-Sep-2018.) |
Ref | Expression |
---|---|
repizf2.1 |
Ref | Expression |
---|---|
repizf2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2733 | . . 3 | |
2 | 1 | rabex 4133 | . 2 |
3 | repizf2lem 4147 | . . . 4 | |
4 | nfcv 2312 | . . . . . 6 | |
5 | nfrab1 2649 | . . . . . 6 | |
6 | 4, 5 | raleqf 2661 | . . . . 5 |
7 | repizf2.1 | . . . . . 6 | |
8 | 7 | repizf 4105 | . . . . 5 |
9 | 6, 8 | syl6bir 163 | . . . 4 |
10 | 3, 9 | syl5bi 151 | . . 3 |
11 | df-rab 2457 | . . . . . 6 | |
12 | nfv 1521 | . . . . . . . 8 | |
13 | 7 | nfex 1630 | . . . . . . . 8 |
14 | 12, 13 | nfan 1558 | . . . . . . 7 |
15 | 14 | nfab 2317 | . . . . . 6 |
16 | 11, 15 | nfcxfr 2309 | . . . . 5 |
17 | 16 | nfeq2 2324 | . . . 4 |
18 | 4, 5 | raleqf 2661 | . . . 4 |
19 | 17, 18 | exbid 1609 | . . 3 |
20 | 10, 19 | sylibd 148 | . 2 |
21 | 2, 20 | vtocle 2804 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wnf 1453 wex 1485 weu 2019 wmo 2020 cab 2156 wral 2448 wrex 2449 crab 2452 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-coll 4104 ax-sep 4107 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rab 2457 df-v 2732 df-in 3127 df-ss 3134 |
This theorem is referenced by: (None) |
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