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Theorem rnun 5283
 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 5280 . . . 4
21dmeqi 5074 . . 3
3 dmun 5079 . . 3
42, 3eqtri 2458 . 2
5 df-rn 4892 . 2
6 df-rn 4892 . . 3
7 df-rn 4892 . . 3
86, 7uneq12i 3501 . 2
94, 5, 83eqtr4i 2468 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   cun 3320  ccnv 4880   cdm 4881   crn 4882 This theorem is referenced by:  imaundi  5287  imaundir  5288  fun  5610  foun  5696  fpr  5917  sbthlem6  7225  fodomr  7261  brwdom2  7544  ordtval  17258  ex-rn  21753  rnpropg  24040  axlowdimlem13  25898 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-cnv 4889  df-dm 4891  df-rn 4892
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