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Theorem 0ima 5251
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 5245 . . 3  |-  ( (/) " A )  C_  ran  (/)
2 rn0 5156 . . 3  |-  ran  (/)  =  (/)
31, 2sseqtri 3366 . 2  |-  ( (/) " A )  C_  (/)
4 0ss 3641 . 2  |-  (/)  C_  ( (/) " A )
53, 4eqssi 3350 1  |-  ( (/) " A )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1653   (/)c0 3613   ran crn 4908   "cima 4910
This theorem is referenced by:  gsumval3  15545  nghmfval  18787  isnghm  18788
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-br 4238  df-opab 4292  df-xp 4913  df-cnv 4915  df-dm 4917  df-rn 4918  df-res 4919  df-ima 4920
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