This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nfi

Description: Deduce that x is not free in ph from the definition. (Contributed by Wolf Lammen, 15-Sep-2021)

		Ref	Expression
	Hypothesis	nfi.1	$⊢ \exists x φ \to \forall x φ$
	Assertion	nfi	$⊢ Ⅎ x φ$

Step	Hyp	Ref	Expression
1		nfi.1	$⊢ \exists x φ \to \forall x φ$
2		df-nf	$⊢ Ⅎ x φ \leftrightarrow (\exists x φ \to \forall x φ)$
3	1 2	mpbir	$⊢ Ⅎ x φ$