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Theorem untuni 30124
 Description: The union of a class is untangled iff all its members are untangled. (Contributed by Scott Fenton, 28-Feb-2011.)
Assertion
Ref Expression
untuni
Distinct variable group:   ,,

Proof of Theorem untuni
StepHypRef Expression
1 r19.23v 2912 . . . 4
21albii 1687 . . 3
3 ralcom4 3106 . . 3
4 eluni2 4226 . . . . 5
54imbi1i 326 . . . 4
65albii 1687 . . 3
72, 3, 63bitr4ri 281 . 2
8 df-ral 2787 . 2
9 df-ral 2787 . . 3
109ralbii 2863 . 2
117, 8, 103bitr4i 280 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187  wal 1435   wcel 1870  wral 2782  wrex 2783  cuni 4222 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-v 3089  df-uni 4223 This theorem is referenced by:  untangtr  30129  dfon2lem3  30218  dfon2lem7  30222
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