Metamath Proof Explorer


Theorem nffv

Description: Bound-variable hypothesis builder for function value. (Contributed by NM, 14-Nov-1995) (Revised by Mario Carneiro, 15-Oct-2016)

Ref Expression
Hypotheses nffv.1 _ x F
nffv.2 _ x A
Assertion nffv _ x F A

Proof

Step Hyp Ref Expression
1 nffv.1 _ x F
2 nffv.2 _ x A
3 df-fv F A = ι y | A F y
4 nfcv _ x y
5 2 1 4 nfbr x A F y
6 5 nfiotaw _ x ι y | A F y
7 3 6 nfcxfr _ x F A