Theorem dfsymdif2 3851

Description: Alternate definition of the symmetric difference. (Contributed by BJ, 30-Apr-2020.)

Assertion

Ref	Expression
dfsymdif2	|- ( A /_\ B ) = { x | ( x e. A \/_ x e. B ) }

Distinct variable groups:   x, A   x, B

Proof of Theorem dfsymdif2

Step	Hyp	Ref	Expression
1		elsymdifxor 3850	. 2 |- ( x e. ( A /_\ B ) <-> ( x e. A \/_ x e. B ) )
2	1	abbi2i 2738	1 |- ( A /_\ B ) = { x | ( x e. A \/_ x e. B ) }

Syntax hints:   \/_ wxo 1464   = wceq 1483   e. wcel 1990   {cab 2608   /_\ csymdif 3843

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-xor 1465  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-un 3579  df-symdif 3844

This theorem is referenced by: (None)