Theorem nfnegd

Description: Deduction version of nfneg . (Contributed by NM, 29-Feb-2008) (Revised by Mario Carneiro, 15-Oct-2016)

	Ref	Expression
Hypothesis	nfnegd.1	$$⊢\phi \to \underset{\_}{Ⅎ}xA$$
Assertion	nfnegd	$$⊢\phi \to \underset{\_}{Ⅎ}x\left(-A\right)$$

Proof

Step	Hyp	Ref	Expression
1		nfnegd.1	$$⊢\phi \to \underset{\_}{Ⅎ}xA$$
2		df-neg	$$⊢-A=0-A$$
3		nfcvd	$$⊢\phi \to \underset{\_}{Ⅎ}x0$$
4		nfcvd	$$⊢\phi \to \underset{\_}{Ⅎ}x-$$
5	3 4 1	nfovd	$$⊢\phi \to \underset{\_}{Ⅎ}x\left(0-A\right)$$
6	2 5	nfcxfrd	$$⊢\phi \to \underset{\_}{Ⅎ}x\left(-A\right)$$