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Theorem untuni 25163
 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 2824 . . . 4
21albii 1576 . . 3
3 ralcom4 2976 . . 3
4 eluni2 4021 . . . . 5
54imbi1i 317 . . . 4
65albii 1576 . . 3
72, 3, 63bitr4ri 271 . 2
8 df-ral 2712 . 2
9 df-ral 2712 . . 3
109ralbii 2731 . 2
117, 8, 103bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550   wcel 1726  wral 2707  wrex 2708  cuni 4017 This theorem is referenced by:  untangtr  25168  dfon2lem3  25417  dfon2lem7  25421 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 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-uni 4018
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