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Mirrors > Home > ILE Home > Th. List > repizf2 | Unicode version |
Description: Replacement. This version of replacement is stronger than repizf 4081 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 4081 with ax-sep 4083. 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 2715 | . . 3 | |
2 | 1 | rabex 4109 | . 2 |
3 | repizf2lem 4123 | . . . 4 | |
4 | nfcv 2299 | . . . . . 6 | |
5 | nfrab1 2636 | . . . . . 6 | |
6 | 4, 5 | raleqf 2648 | . . . . 5 |
7 | repizf2.1 | . . . . . 6 | |
8 | 7 | repizf 4081 | . . . . 5 |
9 | 6, 8 | syl6bir 163 | . . . 4 |
10 | 3, 9 | syl5bi 151 | . . 3 |
11 | df-rab 2444 | . . . . . 6 | |
12 | nfv 1508 | . . . . . . . 8 | |
13 | 7 | nfex 1617 | . . . . . . . 8 |
14 | 12, 13 | nfan 1545 | . . . . . . 7 |
15 | 14 | nfab 2304 | . . . . . 6 |
16 | 11, 15 | nfcxfr 2296 | . . . . 5 |
17 | 16 | nfeq2 2311 | . . . 4 |
18 | 4, 5 | raleqf 2648 | . . . 4 |
19 | 17, 18 | exbid 1596 | . . 3 |
20 | 10, 19 | sylibd 148 | . 2 |
21 | 2, 20 | vtocle 2786 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wnf 1440 wex 1472 weu 2006 wmo 2007 cab 2143 wral 2435 wrex 2436 crab 2439 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-coll 4080 ax-sep 4083 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rab 2444 df-v 2714 df-in 3108 df-ss 3115 |
This theorem is referenced by: (None) |
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