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Theorem f1o0 6642
 Description: One-to-one onto mapping of the empty set. (Contributed by NM, 10-Sep-2004.)
Assertion
Ref Expression
f1o0 ∅:∅–1-1-onto→∅

Proof of Theorem f1o0
StepHypRef Expression
1 eqid 2824 . 2 ∅ = ∅
2 f1o00 6640 . 2 (∅:∅–1-1-onto→∅ ↔ (∅ = ∅ ∧ ∅ = ∅))
31, 1, 2mpbir2an 710 1 ∅:∅–1-1-onto→∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  ∅c0 4276  –1-1-onto→wf1o 6342 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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-br 5053  df-opab 5115  df-id 5447  df-xp 5548  df-rel 5549  df-cnv 5550  df-co 5551  df-dm 5552  df-rn 5553  df-fun 6345  df-fn 6346  df-f 6347  df-f1 6348  df-fo 6349  df-f1o 6350 This theorem is referenced by:  brwdom2  9034  cnfcom  9160  ackbij2lem2  9660  eupth0  28006  f1ocnt  30540  iso0  40936
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