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Theorem ima0 4937
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 4601 . 2  |-  ( A
" (/) )  =  ran  (  A  |`  (/) )
2 res0 4866 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 4812 . 2  |-  ran  (  A  |`  (/) )  =  ran  (/)
4 rn0 4843 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2277 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1619   (/)c0 3362   ran crn 4581    |` cres 4582   "cima 4583
This theorem is referenced by:  relimasn  4943  elimasni  4947  fv2  5373  fvprc  5374  ecexr  6551  domunfican  7014  fodomfi  7020  efgrelexlema  14893  gsumval3  15026  dprdsn  15106  cnindis  16852  cnhaus  16914  cmpfi  16967  xkouni  17126  xkoccn  17145  mbfima  18819  ismbf2d  18828  limcnlp  19060  mdeg0  19288  pserulm  19630  eupath2  23075  funpartfv  23657  inisegn0  26306
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 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108
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 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-br 3921  df-opab 3975  df-xp 4594  df-cnv 4596  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601
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