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Mirrors > Home > NFE Home > Th. List > elimakv | GIF version |
Description: Membership in a Kuratowski image under V. (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
elimak.1 | ⊢ C ∈ V |
Ref | Expression |
---|---|
elimakv | ⊢ (C ∈ (A “k V) ↔ ∃y⟪y, C⟫ ∈ A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elimak.1 | . 2 ⊢ C ∈ V | |
2 | elimakvg 4258 | . 2 ⊢ (C ∈ V → (C ∈ (A “k V) ↔ ∃y⟪y, C⟫ ∈ A)) | |
3 | 1, 2 | ax-mp 8 | 1 ⊢ (C ∈ (A “k V) ↔ ∃y⟪y, C⟫ ∈ A) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ∃wex 1541 ∈ wcel 1710 Vcvv 2859 ⟪copk 4057 “k cimak 4179 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-opk 4058 df-imak 4189 |
This theorem is referenced by: opkelcokg 4261 cokrelk 4284 dfpw12 4301 evenodddisjlem1 4515 dfswap2 4741 |
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