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Theorem 0ima 5185
Description: Image under the empty relation. (Contributed by FL, 11-Jan-2007.)
Assertion
Ref Expression
0ima  |-  ( (/) " A )  =  (/)

Proof of Theorem 0ima
StepHypRef Expression
1 imassrn 5180 . . 3  |-  ( (/) " A )  C_  ran  (/)
2 rn0 5091 . . 3  |-  ran  (/)  =  (/)
31, 2sseqtri 3388 . 2  |-  ( (/) " A )  C_  (/)
4 0ss 3666 . 2  |-  (/)  C_  ( (/) " A )
53, 4eqssi 3372 1  |-  ( (/) " A )  =  (/)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369   (/)c0 3637   ran crn 4841   "cima 4843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4413  ax-nul 4421  ax-pr 4531
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2257  df-mo 2258  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2720  df-rex 2721  df-rab 2724  df-v 2974  df-dif 3331  df-un 3333  df-in 3335  df-ss 3342  df-nul 3638  df-if 3792  df-sn 3878  df-pr 3880  df-op 3884  df-br 4293  df-opab 4351  df-xp 4846  df-cnv 4848  df-dm 4850  df-rn 4851  df-res 4852  df-ima 4853
This theorem is referenced by:  csbrn  5299  gsumval3OLD  16382  nghmfval  20301  isnghm  20302
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