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Theorem 0ima 6034
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 6028 . . 3 (∅ “ 𝐴) ⊆ ran ∅
2 rn0 5885 . . 3 ran ∅ = ∅
31, 2sseqtri 3984 . 2 (∅ “ 𝐴) ⊆ ∅
4 0ss 4360 . 2 ∅ ⊆ (∅ “ 𝐴)
53, 4eqssi 3964 1 (∅ “ 𝐴) = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  c0 4286  ran crn 5638  cima 5640
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5260  ax-nul 5267  ax-pr 5388
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-br 5110  df-opab 5172  df-xp 5643  df-cnv 5645  df-dm 5647  df-rn 5648  df-res 5649  df-ima 5650
This theorem is referenced by:  csbrn  6159  nghmfval  24109  isnghm  24110  mptiffisupp  31661  mthmval  34233  ec0  36880  0he  42146  limsup0  44025  0cnf  44208
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