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Theorem repizf2lem 3914
 Description: Lemma for repizf2 3915. 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.)
Assertion
Ref Expression
repizf2lem

Proof of Theorem repizf2lem
StepHypRef Expression
1 df-mo 1904 . . . 4
21imbi2i 215 . . 3
32albii 1359 . 2
4 df-ral 2311 . 2
5 df-ral 2311 . . 3
6 rabid 2485 . . . . . 6
76imbi1i 227 . . . . 5
8 impexp 250 . . . . 5
97, 8bitri 173 . . . 4
109albii 1359 . . 3
115, 10bitri 173 . 2
123, 4, 113bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241  wex 1381   wcel 1393  weu 1900  wmo 1901  wral 2306  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-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-sb 1646  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311  df-rab 2315 This theorem is referenced by:  repizf2  3915
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