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Theorem f1o0 6749
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 2740 . 2 ∅ = ∅
2 f1o00 6747 . 2 (∅:∅–1-1-onto→∅ ↔ (∅ = ∅ ∧ ∅ = ∅))
31, 1, 2mpbir2an 708 1 ∅:∅–1-1-onto→∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  c0 4262  1-1-ontowf1o 6430
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2711  ax-sep 5227  ax-nul 5234  ax-pr 5356
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-nf 1791  df-sb 2072  df-mo 2542  df-eu 2571  df-clab 2718  df-cleq 2732  df-clel 2818  df-nfc 2891  df-ral 3071  df-rex 3072  df-rab 3075  df-v 3433  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-sn 4568  df-pr 4570  df-op 4574  df-br 5080  df-opab 5142  df-id 5489  df-xp 5595  df-rel 5596  df-cnv 5597  df-co 5598  df-dm 5599  df-rn 5600  df-fun 6433  df-fn 6434  df-f 6435  df-f1 6436  df-fo 6437  df-f1o 6438
This theorem is referenced by:  en0  8784  en0OLD  8785  en0r  8787  brwdom2  9308  cnfcom  9434  ackbij2lem2  9995  eupth0  28572  f1ocnt  31117  iso0  41893
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