Theorem nfsymdif 3848

Description: Hypothesis builder for symmetric difference. (Contributed by Scott Fenton, 19-Feb-2013.) (Revised by Mario Carneiro, 11-Dec-2016.)

Hypotheses

Ref	Expression
nfsymdif.1	|- F/_ x A
nfsymdif.2	|- F/_ x B

Assertion

Ref	Expression
nfsymdif	|- F/_ x ( A /_\ B )

Proof of Theorem nfsymdif

Step	Hyp	Ref	Expression
1		df-symdif 3844	. 2 |- ( A /_\ B ) = ( ( A \ B ) u. ( B \ A ) )
2		nfsymdif.1	. . . 4 |- F/_ x A
3		nfsymdif.2	. . . 4 |- F/_ x B
4	2, 3	nfdif 3731	. . 3 |- F/_ x ( A \ B )
5	3, 2	nfdif 3731	. . 3 |- F/_ x ( B \ A )
6	4, 5	nfun 3769	. 2 |- F/_ x ( ( A \ B ) u. ( B \ A ) )
7	1, 6	nfcxfr 2762	1 |- F/_ x ( A /_\ B )

Syntax hints:   F/_wnfc 2751   \ cdif 3571   u. cun 3572   /_\ 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-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-dif 3577  df-un 3579  df-symdif 3844

This theorem is referenced by: (None)