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Theorem difun1 3593
 Description: A relationship involving double difference and union. (Contributed by NM, 29-Aug-2004.)
Assertion
Ref Expression
difun1

Proof of Theorem difun1
StepHypRef Expression
1 inass 3543 . . . 4
2 invdif 3574 . . . 4
31, 2eqtr3i 2457 . . 3
4 undm 3591 . . . . 5
54ineq2i 3531 . . . 4
6 invdif 3574 . . . 4
75, 6eqtr3i 2457 . . 3
83, 7eqtr3i 2457 . 2
9 invdif 3574 . . 3
109difeq1i 3453 . 2
118, 10eqtr3i 2457 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  cvv 2948   cdif 3309   cun 3310   cin 3311 This theorem is referenced by:  dif32  3596  difabs  3597  infdiffi  7604  mreexexlem4d  13864  nulmbl2  19423  unmbl  19424 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319
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