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Mirrors > Home > ILE Home > Th. List > repizf | Unicode version |
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 4001. It is identical to
zfrep6 4003 except for the choice of a freeness
hypothesis rather than a
distinct variable constraint between ![]() ![]() |
Ref | Expression |
---|---|
ax-coll.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
repizf |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2003 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | ralimi 2467 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | ax-coll.1 |
. . 3
![]() ![]() ![]() ![]() | |
4 | 3 | ax-coll 4001 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | syl 14 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-coll 4001 |
This theorem depends on definitions: df-bi 116 df-nf 1418 df-sb 1717 df-eu 1976 df-ral 2393 |
This theorem is referenced by: zfrep6 4003 repizf2 4044 |
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