Theorem nf5rd

Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	nf5rd.1	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
Assertion	nf5rd	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		nf5rd.1	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
2		nf5r	⊢ ( Ⅎ 𝑥 𝜓 → ( 𝜓 → ∀ 𝑥 𝜓 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) )