Theorem zfrep6 3865

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 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	|- (A.x e. z E!yph -> E.wA.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 1418	. 2 |- F/wph
2	1	repizf 3864	1 |- (A.x e. z E!yph -> E.wA.x e. z E.y e. w ph)

Syntax hints:   -> wi 4  E.wex 1378  E!weu 1897  A.wral 2300  E.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-bndl 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