Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  difun1 Unicode version

Theorem difun1 3367
 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 3317 . . . 4
2 invdif 3349 . . . 4
31, 2eqtr3i 2180 . . 3
4 undm 3365 . . . . 5
54ineq2i 3305 . . . 4
6 invdif 3349 . . . 4
75, 6eqtr3i 2180 . . 3
83, 7eqtr3i 2180 . 2
9 invdif 3349 . . 3
109difeq1i 3221 . 2
118, 10eqtr3i 2180 1
 Colors of variables: wff set class Syntax hints:   wceq 1335  cvv 2712   cdif 3099   cun 3100   cin 3101 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rab 2444  df-v 2714  df-dif 3104  df-un 3106  df-in 3108 This theorem is referenced by:  dif32  3370  difabs  3371  difpr  3698  diffifi  6832  difinfinf  7035
 Copyright terms: Public domain W3C validator