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Theorem 0ima 4805
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 4798 . . 3  |-  ( (/) " A )  C_  ran  (/)
2 rn0 4702 . . 3  |-  ran  (/)  =  (/)
31, 2sseqtri 3059 . 2  |-  ( (/) " A )  C_  (/)
4 0ss 3325 . 2  |-  (/)  C_  ( (/) " A )
53, 4eqssi 3042 1  |-  ( (/) " A )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1290   (/)c0 3287   ran crn 4452   "cima 4454
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-14 1451  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-sep 3963  ax-pow 4015  ax-pr 4045
This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-fal 1296  df-nf 1396  df-sb 1694  df-eu 1952  df-mo 1953  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2622  df-dif 3002  df-un 3004  df-in 3006  df-ss 3013  df-nul 3288  df-pw 3435  df-sn 3456  df-pr 3457  df-op 3459  df-br 3852  df-opab 3906  df-xp 4457  df-cnv 4459  df-dm 4461  df-rn 4462  df-res 4463  df-ima 4464
This theorem is referenced by: (None)
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