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Theorem ima0 4983
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 4647 . 2  |-  ( A
" (/) )  =  ran  (  A  |`  (/) )
2 res0 4912 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 4858 . 2  |-  ran  (  A  |`  (/) )  =  ran  (/)
4 rn0 4889 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2280 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1619   (/)c0 3397   ran crn 4627    |` cres 4628   "cima 4629
This theorem is referenced by:  relimasn  4989  elimasni  4993  fv2  5419  fvprc  5420  ecexr  6598  domunfican  7062  fodomfi  7068  efgrelexlema  14985  gsumval3  15118  dprdsn  15198  cnindis  16947  cnhaus  17009  cmpfi  17062  xkouni  17221  xkoccn  17240  mbfima  18914  ismbf2d  18923  limcnlp  19155  mdeg0  19383  pserulm  19725  eupath2  23241  funpartfv  23823  inisegn0  26472
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237  ax-sep 4081  ax-nul 4089  ax-pr 4152
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121  df-mo 2122  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-rab 2523  df-v 2742  df-dif 3097  df-un 3099  df-in 3101  df-ss 3108  df-nul 3398  df-if 3507  df-sn 3587  df-pr 3588  df-op 3590  df-br 3964  df-opab 4018  df-xp 4640  df-cnv 4642  df-dm 4644  df-rn 4645  df-res 4646  df-ima 4647
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