Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  iso0 Unicode version

Theorem iso0 5711
 Description: The empty set is an isomorphism from the empty set to the empty set. (Contributed by Steve Rodriguez, 24-Oct-2015.)
Assertion
Ref Expression
iso0

Proof of Theorem iso0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 f1o0 5397 . 2
2 ral0 3459 . 2
3 df-isom 5127 . 2
41, 2, 3mpbir2an 926 1
 Colors of variables: wff set class Syntax hints:   wb 104  wral 2414  c0 3358   class class class wbr 3924  wf1o 5117  cfv 5118   wiso 5119 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-nul 4049  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-dif 3068  df-un 3070  df-in 3072  df-ss 3079  df-nul 3359  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-id 4210  df-xp 4540  df-rel 4541  df-cnv 4542  df-co 4543  df-dm 4544  df-rn 4545  df-fun 5120  df-fn 5121  df-f 5122  df-f1 5123  df-fo 5124  df-f1o 5125  df-isom 5127 This theorem is referenced by:  zfz1iso  10577
 Copyright terms: Public domain W3C validator