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Theorem zfrep6 3865
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 3866 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 1418 . 2 wφ
21repizf 3864 1 (x z ∃!yφwx z y w φ)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1378  ∃!weu 1897  wral 2300  wrex 2301
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-coll 3863
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-ral 2305
This theorem is referenced by:  funimaexglem  4925
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