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Theorem disj4im 3270
 Description: A consequence of two classes being disjoint. In classical logic this would be a biconditional. (Contributed by Jim Kingdon, 2-Aug-2018.)
Assertion
Ref Expression
disj4im

Proof of Theorem disj4im
StepHypRef Expression
1 disj3 3266 . . 3
2 eqcom 2039 . . 3
31, 2bitri 173 . 2
4 dfpss2 3023 . . . 4
54simprbi 260 . . 3
65con2i 557 . 2
73, 6sylbi 114 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1242   cdif 2908   cin 2910   wss 2911   wpss 2912  c0 3218 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-ral 2305  df-v 2553  df-dif 2914  df-in 2918  df-pss 2927  df-nul 3219 This theorem is referenced by: (None)
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