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Theorem funcnv0 5918
Description: The converse of the empty set is a function. (Contributed by AV, 7-Jan-2021.)
Assertion
Ref Expression
funcnv0 Fun

Proof of Theorem funcnv0
StepHypRef Expression
1 fun0 5917 . 2 Fun ∅
2 cnv0 5499 . . 3 ∅ = ∅
32funeqi 5873 . 2 (Fun ∅ ↔ Fun ∅)
41, 3mpbir 221 1 Fun
Colors of variables: wff setvar class
Syntax hints:  c0 3896  ccnv 5078  Fun wfun 5846
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4746  ax-nul 4754  ax-pr 4872
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-mo 2474  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rex 2913  df-rab 2916  df-v 3191  df-dif 3562  df-un 3564  df-in 3566  df-ss 3573  df-nul 3897  df-if 4064  df-sn 4154  df-pr 4156  df-op 4160  df-br 4619  df-opab 4679  df-id 4994  df-xp 5085  df-rel 5086  df-cnv 5087  df-co 5088  df-fun 5854
This theorem is referenced by:  pthdlem1  26548  0trl  26866  0pth  26869
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