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Theorem f10 6638
Description: The empty set maps one-to-one into any class. (Contributed by NM, 7-Apr-1998.)
Assertion
Ref Expression
f10 ∅:∅–1-1𝐴

Proof of Theorem f10
StepHypRef Expression
1 f0 6550 . 2 ∅:∅⟶𝐴
2 funcnv0 6408 . 2 Fun
3 df-f1 6348 . 2 (∅:∅–1-1𝐴 ↔ (∅:∅⟶𝐴 ∧ Fun ∅))
41, 2, 3mpbir2an 710 1 ∅:∅–1-1𝐴
Colors of variables: wff setvar class
Syntax hints:  c0 4276  ccnv 5541  Fun wfun 6337  wf 6339  1-1wf1 6340
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
This theorem is referenced by:  f10d  6639  fo00  6641  marypha1lem  8894  hashf1  13820  usgr0  27040
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