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Metamath Proof Explorer

Theorem nf5dv

Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 18-Sep-2021) (Proof shortened by Wolf Lammen, 13-Jul-2022)

		Ref	Expression
	Hypothesis	nf5dv.1	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) )
	Assertion	nf5dv	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		nf5dv.1	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3	2 1	nf5dh	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )