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Theorem ima0 5018
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 4682 . 2  |-  ( A
" (/) )  =  ran  (  A  |`  (/) )
2 res0 4947 . . 3  |-  ( A  |`  (/) )  =  (/)
32rneqi 4893 . 2  |-  ran  (  A  |`  (/) )  =  ran  (/)
4 rn0 4924 . 2  |-  ran  (/)  =  (/)
51, 3, 43eqtri 2282 1  |-  ( A
" (/) )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1619   (/)c0 3430   ran crn 4662    |` cres 4663   "cima 4664
This theorem is referenced by:  relimasn  5024  elimasni  5028  fv2  5454  fvprc  5455  ecexr  6633  domunfican  7097  fodomfi  7103  efgrelexlema  15021  gsumval3  15154  dprdsn  15234  cnindis  16983  cnhaus  17045  cmpfi  17098  xkouni  17257  xkoccn  17276  mbfima  18950  ismbf2d  18959  limcnlp  19191  mdeg0  19419  pserulm  19761  eupath2  23277  funpartfv  23859  inisegn0  26508
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 2239  ax-sep 4115  ax-nul 4123  ax-pr 4186
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 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-rab 2527  df-v 2765  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-nul 3431  df-if 3540  df-sn 3620  df-pr 3621  df-op 3623  df-br 3998  df-opab 4052  df-xp 4675  df-cnv 4677  df-dm 4679  df-rn 4680  df-res 4681  df-ima 4682
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