ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  repizf Structured version   Unicode version

Theorem repizf 3843
Description: Axiom of Replacement. Axiom 7' of [Crosilla], p. "Axioms of CZF and IZF" (with unnecessary quantifier removed). In our context this is not an axiom, but a theorem proved from ax-coll 3842. It is identical to zfrep6 3844 except for the choice of a freeness hypothesis rather than a distinct variable constraint between  b and . (Contributed by Jim Kingdon, 23-Aug-2018.)
Hypothesis
Ref Expression
ax-coll.1  F/ b
Assertion
Ref Expression
repizf  a  b  a  b
Distinct variable group:   ,, a, b
Allowed substitution hints:   (,, a, b)

Proof of Theorem repizf
StepHypRef Expression
1 euex 1908 . . 3
21ralimi 2358 . 2  a  a
3 ax-coll.1 . . 3  F/ b
43ax-coll 3842 . 2  a  b  a  b
52, 4syl 14 1  a  b  a  b
Colors of variables: wff set class
Syntax hints:   wi 4   F/wnf 1325  wex 1358  weu 1878  wral 2280  wrex 2281
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 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-coll 3842
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624  df-eu 1881  df-ral 2285
This theorem is referenced by:  zfrep6  3844  repizf2  3885
  Copyright terms: Public domain W3C validator