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Theorem ima0 5030
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 4702 . 2  |-  ( A
" (/) )  =  ran  ( A  |`  (/) )
2 res0 4959 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 4905 . 2  |-  ran  ( A  |`  (/) )  =  ran  (/)
4 rn0 4936 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2307 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1623   (/)c0 3455   ran crn 4690    |` cres 4691   "cima 4692
This theorem is referenced by:  relimasn  5036  elimasni  5040  dffv3  5521  ecexr  6665  domunfican  7129  fodomfi  7135  efgrelexlema  15058  gsumval3  15191  dprdsn  15271  cnindis  17020  cnhaus  17082  cmpfi  17135  xkouni  17294  xkoccn  17313  mbfima  18987  ismbf2d  18996  limcnlp  19228  mdeg0  19456  pserulm  19798  disjpreima  23361  dstrvprob  23672  eupath2  23904  funpartfv  24483  inisegn0  27140
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-xp 4695  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702
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