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Theorem imaundi 4760
 Description: Distributive law for image over union. Theorem 35 of [Suppes] p. 65. (Contributed by NM, 30-Sep-2002.)
Assertion
Ref Expression
imaundi

Proof of Theorem imaundi
StepHypRef Expression
1 resundi 4647 . . . 4
21rneqi 4584 . . 3
3 rnun 4756 . . 3
42, 3eqtri 2102 . 2
5 df-ima 4378 . 2
6 df-ima 4378 . . 3
7 df-ima 4378 . . 3
86, 7uneq12i 3125 . 2
94, 5, 83eqtr4i 2112 1
 Colors of variables: wff set class Syntax hints:   wceq 1285   cun 2972   crn 4366   cres 4367  cima 4368 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3406  df-pr 3407  df-op 3409  df-br 3788  df-opab 3842  df-xp 4371  df-cnv 4373  df-dm 4375  df-rn 4376  df-res 4377  df-ima 4378 This theorem is referenced by:  fnimapr  5259
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