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Theorem symdifex 4108
 Description: The symmetric difference of two sets is a set. (Contributed by SF, 12-Jan-2015.)
Hypotheses
Ref Expression
boolex.1
boolex.2
Assertion
Ref Expression
symdifex

Proof of Theorem symdifex
StepHypRef Expression
1 boolex.1 . 2
2 boolex.2 . 2
3 symdifexg 4103 . 2
41, 2, 3mp2an 653 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1710  cvv 2859   csymdif 3209 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216 This theorem is referenced by:  addcexlem  4382  nnsucelrlem1  4424  ltfinex  4464  ncfinraiselem2  4480  ncfinlowerlem1  4482  tfinrelkex  4487  evenfinex  4503  oddfinex  4504  evenodddisjlem1  4515  nnadjoinlem1  4519  nnpweqlem1  4522  srelkex  4525  tfinnnlem1  4533  opexg  4587  proj2exg  4592  setconslem5  4735  1stex  4739  swapex  4742  mptexlem  5810  mpt2exlem  5811  extex  5915  ovcelem1  6171  ceex  6174  tcfnex  6244  nmembers1lem1  6268  nchoicelem11  6299  nchoicelem16  6304  nchoicelem18  6306
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