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Theorem rnun 5419
 Description: Distributive law for range over union. Theorem 8 of [Suppes] p. 60. (Contributed by NM, 24-Mar-1998.)
Assertion
Ref Expression
rnun

Proof of Theorem rnun
StepHypRef Expression
1 cnvun 5416 . . . 4
21dmeqi 5209 . . 3
3 dmun 5214 . . 3
42, 3eqtri 2486 . 2
5 df-rn 5015 . 2
6 df-rn 5015 . . 3
7 df-rn 5015 . . 3
86, 7uneq12i 3655 . 2
94, 5, 83eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  u.cun 3473  'ccnv 5003  domcdm 5004  ran`crn 5005 This theorem is referenced by:  imaundi  5423  imaundir  5424  rnpropg  5493  fun  5753  foun  5839  fpr  6079  sbthlem6  7652  fodomr  7688  brwdom2  8020  ordtval  19690  axlowdimlem13  24257  ex-rn  25161  ffsrn  27552  locfinref  27844  ptrest  30048 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-cnv 5012  df-dm 5014  df-rn 5015
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