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Mirrors > Home > NFE Home > Th. List > imagekrelk | GIF version |
Description: The Kuratowski image functor is a relationship. (Contributed by SF, 14-Jan-2015.) |
Ref | Expression |
---|---|
imagekrelk | ⊢ ImagekA ⊆ (V ×k V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-imagek 4194 | . 2 ⊢ ImagekA = ((V ×k V) ∖ (( Ins2k Sk ⊕ Ins3k ( Sk ∘k ◡k SIk A)) “k ℘1℘11c)) | |
2 | difss 3393 | . 2 ⊢ ((V ×k V) ∖ (( Ins2k Sk ⊕ Ins3k ( Sk ∘k ◡k SIk A)) “k ℘1℘11c)) ⊆ (V ×k V) | |
3 | 1, 2 | eqsstri 3301 | 1 ⊢ ImagekA ⊆ (V ×k V) |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 2859 ∖ cdif 3206 ⊕ csymdif 3209 ⊆ wss 3257 1cc1c 4134 ℘1cpw1 4135 ×k cxpk 4174 ◡kccnvk 4175 Ins2k cins2k 4176 Ins3k cins3k 4177 “k cimak 4179 ∘k ccomk 4180 SIk csik 4181 Imagekcimagek 4182 Sk cssetk 4183 |
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-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-ss 3259 df-imagek 4194 |
This theorem is referenced by: (None) |
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