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Theorem imacok 4282
 Description: Image under a composition. (Contributed by SF, 4-Feb-2015.)
Assertion
Ref Expression
imacok k k kk

Proof of Theorem imacok
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 2862 . . . . . 6
2 vex 2862 . . . . . 6
31, 2opkelcok 4262 . . . . 5 k
43rexbii 2639 . . . 4 k
5 rexcom4 2878 . . . 4
6 df-rex 2620 . . . . 5 k k
7 vex 2862 . . . . . . . . 9
87elimak 4259 . . . . . . . 8 k
98anbi1i 676 . . . . . . 7 k
10 r19.41v 2764 . . . . . . 7
119, 10bitr4i 243 . . . . . 6 k
1211exbii 1582 . . . . 5 k
136, 12bitr2i 241 . . . 4 k
144, 5, 133bitri 262 . . 3 k k
152elimak 4259 . . 3 k k k
162elimak 4259 . . 3 kk k
1714, 15, 163bitr4i 268 . 2 k k kk
1817eqriv 2350 1 k k kk
 Colors of variables: wff setvar class Syntax hints:   wa 358  wex 1541   wceq 1642   wcel 1710  wrex 2615  copk 4057  kcimak 4179   k ccomk 4180 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-3an 936  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-rex 2620  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-cnvk 4186  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-cok 4190 This theorem is referenced by: (None)
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