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Theorem symdifcom 3542
 Description: Symmetric difference commutes. (Contributed by SF, 11-Jan-2015.)
Assertion
Ref Expression
symdifcom (AB) = (BA)

Proof of Theorem symdifcom
StepHypRef Expression
1 uncom 3408 . 2 ((A B) ∪ (B A)) = ((B A) ∪ (A B))
2 df-symdif 3216 . 2 (AB) = ((A B) ∪ (B A))
3 df-symdif 3216 . 2 (BA) = ((B A) ∪ (A B))
41, 2, 33eqtr4i 2383 1 (AB) = (BA)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∖ cdif 3206   ∪ cun 3207   ⊕ 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 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-un 3214  df-symdif 3216 This theorem is referenced by: (None)
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