Mathbox for Steve Rodriguez < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  iso0 Unicode version

Theorem iso0 27366
 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 5666 . 2
2 ral0 3689 . 2
3 df-isom 5417 . 2
41, 2, 3mpbir2an 887 1
 Colors of variables: wff set class Syntax hints:   wb 177  wral 2663  c0 3585   class class class wbr 4167  wf1o 5407  cfv 5408   wiso 5409 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382  ax-sep 4285  ax-nul 4293  ax-pr 4358 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2256  df-mo 2257  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2526  df-ne 2566  df-ral 2668  df-rex 2669  df-rab 2672  df-v 2915  df-dif 3280  df-un 3282  df-in 3284  df-ss 3291  df-nul 3586  df-if 3697  df-sn 3777  df-pr 3778  df-op 3780  df-br 4168  df-opab 4222  df-id 4453  df-xp 4838  df-rel 4839  df-cnv 4840  df-co 4841  df-dm 4842  df-rn 4843  df-fun 5410  df-fn 5411  df-f 5412  df-f1 5413  df-fo 5414  df-f1o 5415  df-isom 5417
 Copyright terms: Public domain W3C validator