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Mirrors > Home > NFE Home > Th. List > xpkssvvk | GIF version |
Description: Any Kuratowski cross product is a subset of (V ×k V). (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
xpkssvvk | ⊢ (A ×k B) ⊆ (V ×k V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xpk 4185 | . 2 ⊢ (A ×k B) = {x ∣ ∃y∃z(x = ⟪y, z⟫ ∧ (y ∈ A ∧ z ∈ B))} | |
2 | 1 | opkabssvvki 4209 | 1 ⊢ (A ×k B) ⊆ (V ×k V) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 358 ∈ wcel 1710 Vcvv 2859 ⊆ wss 3257 ×k cxpk 4174 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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 |
This theorem is referenced by: elp6 4263 cnvkxpk 4276 inxpk 4277 |
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