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Theorem 0ima 5110
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 5104 . . 3  |-  ( (/) " A )  C_  ran  (/)
2 rn0 5015 . . 3  |-  ran  (/)  =  (/)
31, 2sseqtri 3286 . 2  |-  ( (/) " A )  C_  (/)
4 0ss 3559 . 2  |-  (/)  C_  ( (/) " A )
53, 4eqssi 3271 1  |-  ( (/) " A )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1642   (/)c0 3531   ran crn 4769   "cima 4771
This theorem is referenced by:  gsumval3  15284  nghmfval  18327  isnghm  18328
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220  ax-nul 4228  ax-pr 4293
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2213  df-mo 2214  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-br 4103  df-opab 4157  df-xp 4774  df-cnv 4776  df-dm 4778  df-rn 4779  df-res 4780  df-ima 4781
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