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Mirrors > Home > ILE Home > Th. List > zfrep6 | GIF version |
Description: A version of the Axiom of Replacement. Normally 𝜑 would have free variables 𝑥 and 𝑦. Axiom 6 of [Kunen] p. 12. The Separation Scheme ax-sep 3978 cannot be derived from this version and must be stated as a separate axiom in an axiom system (such as Kunen's) that uses this version. (Contributed by NM, 10-Oct-2003.) |
Ref | Expression |
---|---|
zfrep6 | ⊢ (∀𝑥 ∈ 𝑧 ∃!𝑦𝜑 → ∃𝑤∀𝑥 ∈ 𝑧 ∃𝑦 ∈ 𝑤 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1473 | . 2 ⊢ Ⅎ𝑤𝜑 | |
2 | 1 | repizf 3976 | 1 ⊢ (∀𝑥 ∈ 𝑧 ∃!𝑦𝜑 → ∃𝑤∀𝑥 ∈ 𝑧 ∃𝑦 ∈ 𝑤 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1433 ∃!weu 1955 ∀wral 2370 ∃wrex 2371 |
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 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-coll 3975 |
This theorem depends on definitions: df-bi 116 df-nf 1402 df-sb 1700 df-eu 1958 df-ral 2375 |
This theorem is referenced by: funimaexglem 5131 |
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