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Theorem difcom 3634
 Description: Swap the arguments of a class difference. (Contributed by NM, 29-Mar-2007.)
Assertion
Ref Expression
difcom ((A B) C ↔ (A C) B)

Proof of Theorem difcom
StepHypRef Expression
1 uncom 3408 . . 3 (BC) = (CB)
21sseq2i 3296 . 2 (A (BC) ↔ A (CB))
3 ssundif 3633 . 2 (A (BC) ↔ (A B) C)
4 ssundif 3633 . 2 (A (CB) ↔ (A C) B)
52, 3, 43bitr3i 266 1 ((A B) C ↔ (A C) B)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∖ cdif 3206   ∪ cun 3207   ⊆ wss 3257 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  df-ss 3259 This theorem is referenced by:  pssdifcom1  3635  pssdifcom2  3636
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