Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  elsymdif Structured version   Unicode version

Theorem elsymdif 25660
 Description: Membership in a symmetric difference. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
elsymdif (++)

Proof of Theorem elsymdif
StepHypRef Expression
1 elun 3480 . . 3
2 eldif 3322 . . . 4
3 eldif 3322 . . . 4
42, 3orbi12i 508 . . 3
51, 4bitri 241 . 2
6 df-symdif 25655 . . 3 (++)
76eleq2i 2499 . 2 (++)
8 xor 862 . 2
95, 7, 83bitr4i 269 1 (++)
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wo 358   wa 359   wcel 1725   cdif 3309   cun 3310  (++)csymdif 25654 This theorem is referenced by:  symdifass  25664  brsymdif  25665 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-un 3317  df-symdif 25655
 Copyright terms: Public domain W3C validator