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Metamath Proof Explorer

Theorem bj-nnfad

Description: Nonfreeness implies the equivalent of ax-5 , deduction form. See nf5rd . (Contributed by BJ, 2-Dec-2023)

		Ref	Expression
	Hypothesis	bj-nnfad.1	$⊢ φ \to Ⅎ' x ψ$
	Assertion	bj-nnfad	$⊢ φ \to (ψ \to \forall x ψ)$

Step	Hyp	Ref	Expression
1		bj-nnfad.1	$⊢ φ \to Ⅎ' x ψ$
2		bj-nnfa	$⊢ Ⅎ' x ψ \to (ψ \to \forall x ψ)$
3	1 2	syl	$⊢ φ \to (ψ \to \forall x ψ)$