Theorem imagekrelk 4274

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

Assertion

Ref	Expression
imagekrelk	|- ImagekA C_ (_V X.k _V)

Proof of Theorem imagekrelk

Step	Hyp	Ref	Expression
1		df-imagek 4195	. 2 |- ImagekA = ((_V X.k _V) \ (( Ins2k Sk (+) Ins3k ( Sk o.k `'k SIk A))"k~P1 ~P1 1c))
2		difss 3394	. 2 |- ((_V X.k _V) \ (( Ins2k Sk (+) Ins3k ( Sk o.k `'k SIk A))"k~P1 ~P1 1c)) C_ (_V X.k _V)
3	1, 2	eqsstri 3302	1 |- ImagekA C_ (_V X.k _V)

Syntax hints:  _Vcvv 2860   \ cdif 3207   (+) csymdif 3210   C_ wss 3258  1_cc1c 4135  ~P₁ cpw1 4136   X._k cxpk 4175  `'_kccnvk 4176   Ins2_k cins2k 4177   Ins3_k cins3k 4178  "_kcimak 4180   o._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)