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Theorem 0ima 6066
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 6060 . . 3 (∅ “ 𝐴) ⊆ ran ∅
2 rn0 5917 . . 3 ran ∅ = ∅
31, 2sseqtri 4014 . 2 (∅ “ 𝐴) ⊆ ∅
4 0ss 4392 . 2 ∅ ⊆ (∅ “ 𝐴)
53, 4eqssi 3994 1 (∅ “ 𝐴) = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  c0 4318  ran crn 5670  cima 5672
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2702  ax-sep 5292  ax-nul 5299  ax-pr 5420
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-ral 3061  df-rex 3070  df-rab 3432  df-v 3475  df-dif 3947  df-un 3949  df-in 3951  df-ss 3961  df-nul 4319  df-if 4523  df-sn 4623  df-pr 4625  df-op 4629  df-br 5142  df-opab 5204  df-xp 5675  df-cnv 5677  df-dm 5679  df-rn 5680  df-res 5681  df-ima 5682
This theorem is referenced by:  csbrn  6191  nghmfval  24168  isnghm  24169  mptiffisupp  31786  mthmval  34397  ec0  37043  0he  42304  limsup0  44183  0cnf  44366
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