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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 4104. It is identical to zfrep6 4106 except for the choice of a freeness hypothesis rather than a disjoint variable condition between and . (Contributed by Jim Kingdon, 23-Aug-2018.) |
Ref | Expression |
---|---|
ax-coll.1 |
Ref | Expression |
---|---|
repizf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2049 | . . 3 | |
2 | 1 | ralimi 2533 | . 2 |
3 | ax-coll.1 | . . 3 | |
4 | 3 | ax-coll 4104 | . 2 |
5 | 2, 4 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wnf 1453 wex 1485 weu 2019 wral 2448 wrex 2449 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-coll 4104 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-eu 2022 df-ral 2453 |
This theorem is referenced by: zfrep6 4106 repizf2 4148 |
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