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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 4038. It is identical to zfrep6 4040 except for the choice of a freeness hypothesis rather than a distinct variable constraint between and . (Contributed by Jim Kingdon, 23-Aug-2018.) |
Ref | Expression |
---|---|
ax-coll.1 |
Ref | Expression |
---|---|
repizf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2027 | . . 3 | |
2 | 1 | ralimi 2493 | . 2 |
3 | ax-coll.1 | . . 3 | |
4 | 3 | ax-coll 4038 | . 2 |
5 | 2, 4 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wnf 1436 wex 1468 weu 1997 wral 2414 wrex 2415 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-coll 4038 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-eu 2000 df-ral 2419 |
This theorem is referenced by: zfrep6 4040 repizf2 4081 |
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