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Theorem rn0 4936
 Description: The range of the empty set is empty. Part of Theorem 3.8(v) of [Monk1] p. 36. (Contributed by NM, 4-Jul-1994.)
Assertion
Ref Expression
rn0

Proof of Theorem rn0
StepHypRef Expression
1 dm0 4892 . 2
2 dm0rn0 4895 . 2
31, 2mpbi 199 1
 Colors of variables: wff set class Syntax hints:   wceq 1623  c0 3455   cdm 4689   crn 4690 This theorem is referenced by:  ima0  5030  0ima  5031  rnxpid  5109  f0  5425  2ndval  6125  frxp  6225  oarec  6560  map0e  6805  fodomr  7012  dfac5lem3  7752  itunitc  8047  0rest  13334  arwval  13875  oppglsm  14953  mpfrcl  19402  0ngrp  20878  bafval  21160  xpima  23202  0alg  25756  mzpmfp  26825  pmtrfrn  27400  nbgra0edg  28147  uvtx01vtx  28164 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-cnv 4697  df-dm 4699  df-rn 4700
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