Theorem imagekrelk 4274

Description: The Kuratowski image functor is a relationship. (Contributed by SF, 14-Jan-2015.)

Assertion

Ref	Expression
imagekrelk	⊢ ImagekA ⊆ (V ×k V)

Proof of Theorem imagekrelk

Step	Hyp	Ref	Expression
1		df-imagek 4195	. 2 ⊢ ImagekA = ((V ×k V) ∖ (( Ins2k Sk ⊕ Ins3k ( Sk ∘k ◡k SIk A)) “k ℘1℘11c))
2		difss 3394	. 2 ⊢ ((V ×k V) ∖ (( Ins2k Sk ⊕ Ins3k ( Sk ∘k ◡k SIk A)) “k ℘1℘11c)) ⊆ (V ×k V)
3	1, 2	eqsstri 3302	1 ⊢ ImagekA ⊆ (V ×k V)

Syntax hints:  Vcvv 2860   ∖ cdif 3207   ⊕ csymdif 3210   ⊆ wss 3258  1_cc1c 4135  ℘₁cpw1 4136   ×_k cxpk 4175  ^◡_kccnvk 4176   Ins2_k cins2k 4177   Ins3_k cins3k 4178   “_k cimak 4180   ∘_k ccomk 4181   SI_k csik 4182  Image_kcimagek 4183   S_k cssetk 4184

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

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 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-dif 3216  df-ss 3260  df-imagek 4195

This theorem is referenced by: (None)