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Theorem repizf2 3915
 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.)
Hypothesis
Ref Expression
repizf2.1
Assertion
Ref Expression
repizf2
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)

Proof of Theorem repizf2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2560 . . 3
21rabex 3901 . 2
3 repizf2lem 3914 . . . 4
4 nfcv 2178 . . . . . 6
5 nfrab1 2489 . . . . . 6
64, 5raleqf 2501 . . . . 5
7 repizf2.1 . . . . . 6
87repizf 3873 . . . . 5
96, 8syl6bir 153 . . . 4
103, 9syl5bi 141 . . 3
11 df-rab 2315 . . . . . 6
12 nfv 1421 . . . . . . . 8
137nfex 1528 . . . . . . . 8
1412, 13nfan 1457 . . . . . . 7
1514nfab 2182 . . . . . 6
1611, 15nfcxfr 2175 . . . . 5
1716nfeq2 2189 . . . 4
184, 5raleqf 2501 . . . 4
1917, 18exbid 1507 . . 3
2010, 19sylibd 138 . 2
212, 20vtocle 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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