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Theorem ima0 5161
Description: Image of the empty set. Theorem 3.16(ii) of [Monk1] p. 38. (Contributed by NM, 20-May-1998.)
Assertion
Ref Expression
ima0  |-  ( A
" (/) )  =  (/)

Proof of Theorem ima0
StepHypRef Expression
1 df-ima 4831 . 2  |-  ( A
" (/) )  =  ran  ( A  |`  (/) )
2 res0 5090 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 5036 . 2  |-  ran  ( A  |`  (/) )  =  ran  (/)
4 rn0 5067 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2411 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1649   (/)c0 3571   ran crn 4819    |` cres 4820   "cima 4821
This theorem is referenced by:  relimasn  5167  elimasni  5171  dffv3  5664  ecexr  6846  domunfican  7315  fodomfi  7321  efgrelexlema  15308  gsumval3  15441  dprdsn  15521  cnindis  17278  cnhaus  17340  cmpfi  17393  xkouni  17552  xkoccn  17572  mbfima  19391  ismbf2d  19400  limcnlp  19632  mdeg0  19860  pserulm  20205  0pth  21424  spthispth  21427  1pthonlem2  21438  eupath2  21550  disjpreima  23870  imadifxp  23881  dstrvprob  24508  funpartlem  25505  inisegn0  26809
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2242  df-mo 2243  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-br 4154  df-opab 4208  df-xp 4824  df-cnv 4826  df-dm 4828  df-rn 4829  df-res 4830  df-ima 4831
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