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
|- F/_ x F
nffv.2
|- F/_ x A
Assertion nffv
|- F/_ x ( F ` A )

Proof

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