Theorem zfrep6 4150

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 4151 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 1542	. 2 |- F/ w ph
2	1	repizf 4149	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 1506   E!weu 2045   A.wral 2475   E.wrex 2476

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-coll 4148

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-eu 2048  df-ral 2480

This theorem is referenced by:  funimaexglem  5341