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Mirrors > Home > ILE Home > Th. List > repizf2 | Unicode version |
Description: Replacement. This version of replacement is stronger than repizf 3873 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 3873 with ax-sep 3875. 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 2560 | . . 3 | |
2 | 1 | rabex 3901 | . 2 |
3 | repizf2lem 3914 | . . . 4 | |
4 | nfcv 2178 | . . . . . 6 | |
5 | nfrab1 2489 | . . . . . 6 | |
6 | 4, 5 | raleqf 2501 | . . . . 5 |
7 | repizf2.1 | . . . . . 6 | |
8 | 7 | repizf 3873 | . . . . 5 |
9 | 6, 8 | syl6bir 153 | . . . 4 |
10 | 3, 9 | syl5bi 141 | . . 3 |
11 | df-rab 2315 | . . . . . 6 | |
12 | nfv 1421 | . . . . . . . 8 | |
13 | 7 | nfex 1528 | . . . . . . . 8 |
14 | 12, 13 | nfan 1457 | . . . . . . 7 |
15 | 14 | nfab 2182 | . . . . . 6 |
16 | 11, 15 | nfcxfr 2175 | . . . . 5 |
17 | 16 | nfeq2 2189 | . . . 4 |
18 | 4, 5 | raleqf 2501 | . . . 4 |
19 | 17, 18 | exbid 1507 | . . 3 |
20 | 10, 19 | sylibd 138 | . 2 |
21 | 2, 20 | vtocle 2627 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wnf 1349 wex 1381 weu 1900 wmo 1901 cab 2026 wral 2306 wrex 2307 crab 2310 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-coll 3872 ax-sep 3875 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rab 2315 df-v 2559 df-in 2924 df-ss 2931 |
This theorem is referenced by: (None) |
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