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	⊢ Ⅎ 𝑥 𝐴
	nfima.2	⊢ Ⅎ 𝑥 𝐵
Assertion	nfima	⊢ Ⅎ 𝑥 ( 𝐴 “ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		nfima.1	⊢ Ⅎ 𝑥 𝐴
2		nfima.2	⊢ Ⅎ 𝑥 𝐵
3		df-ima	⊢ ( 𝐴 “ 𝐵 ) = ran ( 𝐴 ↾ 𝐵 )
4	1 2	nfres	⊢ Ⅎ 𝑥 ( 𝐴 ↾ 𝐵 )
5	4	nfrn	⊢ Ⅎ 𝑥 ran ( 𝐴 ↾ 𝐵 )
6	3 5	nfcxfr	⊢ Ⅎ 𝑥 ( 𝐴 “ 𝐵 )