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Theorem funcnvcnv 6165
Description: The double converse of a function is a function. (Contributed by NM, 21-Sep-2004.)
Assertion
Ref Expression
funcnvcnv (Fun 𝐴 → Fun 𝐴)

Proof of Theorem funcnvcnv
StepHypRef Expression
1 cnvcnvss 5803 . 2 𝐴𝐴
2 funss 6118 . 2 (𝐴𝐴 → (Fun 𝐴 → Fun 𝐴))
31, 2ax-mp 5 1 (Fun 𝐴 → Fun 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3767  ccnv 5309  Fun wfun 6093
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2354  ax-ext 2775  ax-sep 4973  ax-nul 4981  ax-pr 5095
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-mo 2590  df-eu 2607  df-clab 2784  df-cleq 2790  df-clel 2793  df-nfc 2928  df-ral 3092  df-rab 3096  df-v 3385  df-dif 3770  df-un 3772  df-in 3774  df-ss 3781  df-nul 4114  df-if 4276  df-sn 4367  df-pr 4369  df-op 4373  df-br 4842  df-opab 4904  df-xp 5316  df-rel 5317  df-cnv 5318  df-co 5319  df-fun 6101
This theorem is referenced by:  funcnvres2  6178  inpreima  6566  difpreima  6567  f1oresrab  6619  sbthlem8  8317  fin1a2lem7  9514  cnclima  21398  iscncl  21399  qtopcld  21842  qtoprest  21846  qtopcmap  21848  rnelfmlem  22081  fmfnfmlem3  22085  mbfimaicc  23736  ismbf3d  23759  i1fd  23786  gsummpt2co  30288
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