Theorem nfnd

Description: Deduction associated with nfnt . (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypothesis	nfnd.1	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
Assertion	nfnd	⊢ ( 𝜑 → Ⅎ 𝑥 ¬ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		nfnd.1	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
2		nfnt	⊢ ( Ⅎ 𝑥 𝜓 → Ⅎ 𝑥 ¬ 𝜓 )
3	1 2	syl	⊢ ( 𝜑 → Ⅎ 𝑥 ¬ 𝜓 )