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Theorem ima0 5029
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 4701 . 2  |-  ( A
" (/) )  =  ran  (  A  |`  (/) )
2 res0 4958 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 4904 . 2  |-  ran  (  A  |`  (/) )  =  ran  (/)
4 rn0 4935 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2308 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1623   (/)c0 3456   ran crn 4689    |` cres 4690   "cima 4691
This theorem is referenced by:  relimasn  5035  elimasni  5039  fv2  5482  fvprc  5483  ecexr  6661  domunfican  7125  fodomfi  7131  efgrelexlema  15054  gsumval3  15187  dprdsn  15267  cnindis  17016  cnhaus  17078  cmpfi  17131  xkouni  17290  xkoccn  17309  mbfima  18983  ismbf2d  18992  limcnlp  19224  mdeg0  19452  pserulm  19794  eupath2  23311  funpartfv  23893  inisegn0  26551
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 1636  ax-8 1644  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pr 4213
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 1631  df-eu 2148  df-mo 2149  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-rab 2553  df-v 2791  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-if 3567  df-sn 3647  df-pr 3648  df-op 3650  df-br 4025  df-opab 4079  df-xp 4694  df-cnv 4696  df-dm 4698  df-rn 4699  df-res 4700  df-ima 4701
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