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Mirrors > Home > NFE Home > Th. List > sikssvvk | GIF version |
Description: A Kuratowski singleton image is a Kuratowski relationship. (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
sikssvvk | ⊢ SIk A ⊆ (V ×k V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sik 4192 | . 2 ⊢ SIk A = {x ∣ ∃y∃z(x = ⟪y, z⟫ ∧ ∃t∃u(y = {t} ∧ z = {u} ∧ ⟪t, u⟫ ∈ A))} | |
2 | 1 | opkabssvvki 4209 | 1 ⊢ SIk A ⊆ (V ×k V) |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 934 ∃wex 1541 = wceq 1642 ∈ wcel 1710 Vcvv 2859 ⊆ wss 3257 {csn 3737 ⟪copk 4057 ×k cxpk 4174 SIk csik 4181 |
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 ax-nin 4078 ax-sn 4087 |
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-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-pr 3742 df-opk 4058 df-xpk 4185 df-sik 4192 |
This theorem is referenced by: sikss1c1c 4267 |
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