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Theorem ima0 5213
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 4883 . 2  |-  ( A
" (/) )  =  ran  ( A  |`  (/) )
2 res0 5142 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 5088 . 2  |-  ran  ( A  |`  (/) )  =  ran  (/)
4 rn0 5119 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2459 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1652   (/)c0 3620   ran crn 4871    |` cres 4872   "cima 4873
This theorem is referenced by:  relimasn  5219  elimasni  5223  dffv3  5716  ecexr  6902  domunfican  7371  fodomfi  7377  efgrelexlema  15373  gsumval3  15506  dprdsn  15586  cnindis  17348  cnhaus  17410  cmpfi  17463  xkouni  17623  xkoccn  17643  mbfima  19516  ismbf2d  19525  limcnlp  19757  mdeg0  19985  pserulm  20330  0pth  21562  spthispth  21565  1pthonlem2  21582  eupath2  21694  disjpreima  24018  imadifxp  24030  dstrvprob  24721  opelco3  25395  funpartlem  25779  inisegn0  27109
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-xp 4876  df-cnv 4878  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883
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