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Theorem ima0 5180
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 4850 . 2  |-  ( A
" (/) )  =  ran  ( A  |`  (/) )
2 res0 5109 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 5055 . 2  |-  ran  ( A  |`  (/) )  =  ran  (/)
4 rn0 5086 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2428 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1649   (/)c0 3588   ran crn 4838    |` cres 4839   "cima 4840
This theorem is referenced by:  relimasn  5186  elimasni  5190  dffv3  5683  ecexr  6869  domunfican  7338  fodomfi  7344  efgrelexlema  15336  gsumval3  15469  dprdsn  15549  cnindis  17310  cnhaus  17372  cmpfi  17425  xkouni  17584  xkoccn  17604  mbfima  19477  ismbf2d  19486  limcnlp  19718  mdeg0  19946  pserulm  20291  0pth  21523  spthispth  21526  1pthonlem2  21543  eupath2  21655  disjpreima  23979  imadifxp  23991  dstrvprob  24682  funpartlem  25695  inisegn0  27008
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 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363
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 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-br 4173  df-opab 4227  df-xp 4843  df-cnv 4845  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850
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