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Theorem ima0 5032
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 4704 . 2  |-  ( A
" (/) )  =  ran  ( A  |`  (/) )
2 res0 4961 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 4907 . 2  |-  ran  ( A  |`  (/) )  =  ran  (/)
4 rn0 4938 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2309 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1625   (/)c0 3457   ran crn 4692    |` cres 4693   "cima 4694
This theorem is referenced by:  relimasn  5038  elimasni  5042  dffv3  5523  ecexr  6667  domunfican  7131  fodomfi  7137  efgrelexlema  15060  gsumval3  15193  dprdsn  15273  cnindis  17022  cnhaus  17084  cmpfi  17137  xkouni  17296  xkoccn  17315  mbfima  18989  ismbf2d  18998  limcnlp  19230  mdeg0  19458  pserulm  19800  disjpreima  23363  dstrvprob  23674  eupath2  23906  funpartfv  24485  inisegn0  27151
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-14 1690  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266  ax-sep 4143  ax-nul 4151  ax-pr 4216
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-eu 2149  df-mo 2150  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-ne 2450  df-rab 2554  df-v 2792  df-dif 3157  df-un 3159  df-in 3161  df-ss 3168  df-nul 3458  df-if 3568  df-sn 3648  df-pr 3649  df-op 3651  df-br 4026  df-opab 4080  df-xp 4697  df-cnv 4699  df-dm 4701  df-rn 4702  df-res 4703  df-ima 4704
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