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Theorem zfrep6 3848
Description: A version of the Axiom of Replacement. Normally φ would have free variables x and y. Axiom 6 of [Kunen] p. 12. The Separation Scheme ax-sep 3849 cannot be derived from this version and must be stated as a separate axiom in an axiom system (such as Kunen's) that uses this version. (Contributed by NM, 10-Oct-2003.)
Assertion
Ref Expression
zfrep6 (x z ∃!yφwx z y w φ)
Distinct variable groups:   φ,w   x,y,z,w
Allowed substitution hints:   φ(x,y,z)

Proof of Theorem zfrep6
StepHypRef Expression
1 nfv 1402 . 2 wφ
21repizf 3847 1 (x z ∃!yφwx z y w φ)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1362  ∃!weu 1882  wral 2284  wrex 2285
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-coll 3846
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-eu 1885  df-ral 2289
This theorem is referenced by:  funimaexglem  4908
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