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Theorem 0ima 5341
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 5336 . . 3  |-  ( (/) " A )  C_  ran  (/)
2 rn0 5243 . . 3  |-  ran  (/)  =  (/)
31, 2sseqtri 3521 . 2  |-  ( (/) " A )  C_  (/)
4 0ss 3813 . 2  |-  (/)  C_  ( (/) " A )
53, 4eqssi 3505 1  |-  ( (/) " A )  =  (/)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1398   (/)c0 3783   ran crn 4989   "cima 4991
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-9 1827  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-sep 4560  ax-nul 4568  ax-pr 4676
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-eu 2288  df-mo 2289  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-br 4440  df-opab 4498  df-xp 4994  df-cnv 4996  df-dm 4998  df-rn 4999  df-res 5000  df-ima 5001
This theorem is referenced by:  csbrn  5452  gsumval3OLD  17107  nghmfval  21395  isnghm  21396  mthmval  29199  0cnf  31918  mbf0  31995  0he  38255
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