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Theorem difun1 3676
 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 3615 . . . 4
2 invdif 3657 . . . 4
31, 2eqtr3i 2452 . . 3
4 undm 3674 . . . . 5
54ineq2i 3604 . . . 4
6 invdif 3657 . . . 4
75, 6eqtr3i 2452 . . 3
83, 7eqtr3i 2452 . 2
9 invdif 3657 . . 3
109difeq1i 3522 . 2
118, 10eqtr3i 2452 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437  cvv 3022   cdif 3376   cun 3377   cin 3378 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719  df-rab 2723  df-v 3024  df-dif 3382  df-un 3384  df-in 3386 This theorem is referenced by:  dif32  3679  difabs  3680  difpr  4082  infdiffi  8115  mreexexlem4d  15496  nulmbl2  22432  unmbl  22433  caragenuncllem  38184
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