Theorem nfima

Description: Bound-variable hypothesis builder for image. (Contributed by NM, 30-Dec-1996) (Proof shortened by Andrew Salmon, 27-Aug-2011)

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

Proof

Step	Hyp	Ref	Expression
1		nfima.1	|- F/_ x A
2		nfima.2	|- F/_ x B
3		df-ima	|- ( A " B ) = ran ( A |` B )
4	1 2	nfres	|- F/_ x ( A |` B )
5	4	nfrn	|- F/_ x ran ( A |` B )
6	3 5	nfcxfr	|- F/_ x ( A " B )