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Theorem iso0 27625
 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 5747 . 2
2 ral0 3760 . 2
3 df-isom 5498 . 2
41, 2, 3mpbir2an 888 1
 Colors of variables: wff set class Syntax hints:   wb 178  wral 2712  c0 3616   class class class wbr 4243  wf1o 5488  cfv 5489   wiso 5490 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4361  ax-nul 4369  ax-pr 4438 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rex 2718  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3768  df-sn 3849  df-pr 3850  df-op 3852  df-br 4244  df-opab 4298  df-id 4533  df-xp 4919  df-rel 4920  df-cnv 4921  df-co 4922  df-dm 4923  df-rn 4924  df-fun 5491  df-fn 5492  df-f 5493  df-f1 5494  df-fo 5495  df-f1o 5496  df-isom 5498
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