Theorem nfun

Description: Bound-variable hypothesis builder for the union of classes. (Contributed by NM, 15-Sep-2003) (Revised by Mario Carneiro, 14-Oct-2016)

	Ref	Expression
Hypotheses	nfun.1	|- F/_ x A
	nfun.2	|- F/_ x B
Assertion	nfun	|- F/_ x ( A u. B )

Proof

Step	Hyp	Ref	Expression
1		nfun.1	|- F/_ x A
2		nfun.2	|- F/_ x B
3		df-un	|- ( A u. B ) = { y | ( y e. A \/ y e. B ) }
4	1	nfcri	|- F/ x y e. A
5	2	nfcri	|- F/ x y e. B
6	4 5	nfor	|- F/ x ( y e. A \/ y e. B )
7	6	nfab	|- F/_ x { y | ( y e. A \/ y e. B ) }
8	3 7	nfcxfr	|- F/_ x ( A u. B )