![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 4136. It is identical to
zfrep6 4138 except for the choice of a freeness
hypothesis rather than a
disjoint variable condition between ![]() ![]() |
Ref | Expression |
---|---|
ax-coll.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
repizf |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2068 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | ralimi 2553 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | ax-coll.1 |
. . 3
![]() ![]() ![]() ![]() | |
4 | 3 | ax-coll 4136 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | syl 14 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-coll 4136 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-eu 2041 df-ral 2473 |
This theorem is referenced by: zfrep6 4138 repizf2 4183 |
Copyright terms: Public domain | W3C validator |