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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 ⊢ Ⅎ _ x F
nffv.2 ⊢ Ⅎ _ x A
Assertion nffv ⊢ Ⅎ _ x F ⁡ A

Proof

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