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Theorem repizf 3873
 Description: Axiom of Replacement. Axiom 7' of [Crosilla], p. "Axioms of CZF and IZF" (with unnecessary quantifier removed). In our context this is not an axiom, but a theorem proved from ax-coll 3872. It is identical to zfrep6 3874 except for the choice of a freeness hypothesis rather than a distinct variable constraint between and . (Contributed by Jim Kingdon, 23-Aug-2018.)
Hypothesis
Ref Expression
ax-coll.1
Assertion
Ref Expression
repizf
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)

Proof of Theorem repizf
StepHypRef Expression
1 euex 1930 . . 3
21ralimi 2384 . 2
3 ax-coll.1 . . 3
43ax-coll 3872 . 2
52, 4syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4  wnf 1349  wex 1381  weu 1900  wral 2306  wrex 2307 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-coll 3872 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-ral 2311 This theorem is referenced by:  zfrep6  3874  repizf2  3915
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