MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  f1o0 Structured version   Unicode version

Theorem f1o0 5704
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 2435 . 2  |-  (/)  =  (/)
2 f1o00 5702 . 2  |-  ( (/) :
(/)
-1-1-onto-> (/)  <->  (
(/)  =  (/)  /\  (/)  =  (/) ) )
31, 1, 2mpbir2an 887 1  |-  (/) : (/) -1-1-onto-> (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1652   (/)c0 3620   -1-1-onto->wf1o 5445
This theorem is referenced by:  brwdom2  7533  cnfcom  7649  ackbij2lem2  8112  eupa0  21688  iso0  27504
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453
  Copyright terms: Public domain W3C validator