Theorem nf5rOLD

Description: Obsolete version of nfrd as of 23-Nov-2023. (Contributed by Mario Carneiro, 26-Sep-2016) df-nf changed. (Revised by Wolf Lammen, 11-Sep-2021) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	nf5rOLD	$$⊢Ⅎx\phi \to \left(\phi \to \forall x\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.8a	$$⊢\phi \to \exists x\phi$$
2		df-nf	$$⊢Ⅎx\phi \leftrightarrow \left(\exists x\phi \to \forall x\phi \right)$$
3	2	biimpi	$$⊢Ⅎx\phi \to \left(\exists x\phi \to \forall x\phi \right)$$
4	1 3	syl5	$$⊢Ⅎx\phi \to \left(\phi \to \forall x\phi \right)$$