Theorem zfrep6 4106

Description: A version of the Axiom of Replacement. Normally ph would have free variables x and y. Axiom 6 of [Kunen] p. 12. The Separation Scheme ax-sep 4107 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	|- ( A. x e. z E! y ph -> E. w A. x e. z E. y e. w ph )

Distinct variable groups:   ph, w   x, y, z, w

Allowed substitution hints:   ph( x, y, z)

Proof of Theorem zfrep6

Step	Hyp	Ref	Expression
1		nfv 1521	. 2 |- F/ w ph
2	1	repizf 4105	1 |- ( A. x e. z E! y ph -> E. w A. x e. z E. y e. w ph )

Syntax hints:   -> wi 4   E.wex 1485   E!weu 2019   A.wral 2448   E.wrex 2449

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-coll 4104

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-eu 2022  df-ral 2453

This theorem is referenced by:  funimaexglem  5281