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Theorem chocnul 24863
 Description: Orthogonal complement of the empty set. (Contributed by NM, 31-Oct-2000.) (New usage is discouraged.)
Assertion
Ref Expression
chocnul

Proof of Theorem chocnul
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ral0 3879 . . 3
2 0ss 3761 . . . 4
3 ocel 24816 . . . 4
42, 3ax-mp 5 . . 3
51, 4mpbiran2 910 . 2
65eqriv 2447 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1370   wcel 1758  wral 2793   wss 3423  c0 3732  cfv 5513  (class class class)co 6187  cc0 9380  chil 24453   csp 24456  cort 24464 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4508  ax-nul 4516  ax-pr 4626  ax-hilex 24533 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-ne 2644  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3067  df-sbc 3282  df-dif 3426  df-un 3428  df-in 3430  df-ss 3437  df-nul 3733  df-if 3887  df-pw 3957  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4187  df-br 4388  df-opab 4446  df-mpt 4447  df-id 4731  df-xp 4941  df-rel 4942  df-cnv 4943  df-co 4944  df-dm 4945  df-iota 5476  df-fun 5515  df-fv 5521  df-ov 6190  df-oc 24787 This theorem is referenced by: (None)
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