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Theorem rn0 4952
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  |-  ran  (/)  =  (/)

Proof of Theorem rn0
StepHypRef Expression
1 dm0 4908 . 2  |-  dom  (/)  =  (/)
2 dm0rn0 4911 . 2  |-  ( dom  (/)  =  (/)  <->  ran  (/)  =  (/) )
31, 2mpbi 199 1  |-  ran  (/)  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1632   (/)c0 3468   dom cdm 4705   ran crn 4706
This theorem is referenced by:  ima0  5046  0ima  5047  rnxpid  5125  f0  5441  2ndval  6141  frxp  6241  oarec  6576  map0e  6821  fodomr  7028  dfac5lem3  7768  itunitc  8063  0rest  13350  arwval  13891  oppglsm  14969  mpfrcl  19418  0ngrp  20894  bafval  21176  xpima  23217  0alg  25859  mzpmfp  26928  pmtrfrn  27503  nbgra0edg  28281  uvtx01vtx  28305
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-cnv 4713  df-dm 4715  df-rn 4716
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