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Theorem dif32 3517
 Description: Swap second and third argument of double difference. (Contributed by NM, 18-Aug-2004.)
Assertion
Ref Expression
dif32 ((A B) C) = ((A C) B)

Proof of Theorem dif32
StepHypRef Expression
1 uncom 3408 . . 3 (BC) = (CB)
21difeq2i 3382 . 2 (A (BC)) = (A (CB))
3 difun1 3514 . 2 (A (BC)) = ((A B) C)
4 difun1 3514 . 2 (A (CB)) = ((A C) B)
52, 3, 43eqtr3i 2381 1 ((A B) C) = ((A C) B)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∖ cdif 3206   ∪ cun 3207 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215 This theorem is referenced by:  difdifdir  3637
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