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

Theorem undifabs 3706
 Description: Absorption of difference by union. (Contributed by NM, 18-Aug-2013.)
Assertion
Ref Expression
undifabs

Proof of Theorem undifabs
StepHypRef Expression
1 undif3 3603 . 2
2 unidm 3491 . . 3
32difeq1i 3462 . 2
4 difdif 3474 . 2
51, 3, 43eqtri 2461 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   cdif 3318   cun 3319 This theorem is referenced by:  dfif5  3752 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326
 Copyright terms: Public domain W3C validator