Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dif32 Unicode version

Theorem dif32 3760
 Description: Swap second and third argument of double difference. (Contributed by NM, 18-Aug-2004.)
Assertion
Ref Expression
dif32

Proof of Theorem dif32
StepHypRef Expression
1 uncom 3647 . . 3
21difeq2i 3618 . 2
3 difun1 3757 . 2
4 difun1 3757 . 2
52, 3, 43eqtr3i 2494 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  \cdif 3472  u.cun 3473 This theorem is referenced by:  difdifdir  3915  difsnen  7619  cusgrares  24472 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482
 Copyright terms: Public domain W3C validator