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Theorem elsymdif 3698
 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 3606 . . 3
2 eldif 3446 . . . 4
3 eldif 3446 . . . 4
42, 3orbi12i 523 . . 3
51, 4bitri 252 . 2
6 df-symdif 3693 . . 3
76eleq2i 2499 . 2
8 xor 899 . 2
95, 7, 83bitr4i 280 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187   wo 369   wa 370   wcel 1872   cdif 3433   cun 3434   csymdif 3692 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-v 3082  df-dif 3439  df-un 3441  df-symdif 3693 This theorem is referenced by:  elsymdifxor  3699  symdifass  3702  brsymdif  4480
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