Theorem hbsbwOLD

Description: Obsolete version of hbsbw as of 23-May-2024. (Contributed by NM, 12-Aug-1993) (Revised by Gino Giotto, 10-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	hbsbwOLD.1	$$⊢\phi \to \forall z\phi$$
Assertion	hbsbwOLD	$$⊢\left[y/x\right]\phi \to \forall z\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		hbsbwOLD.1	$$⊢\phi \to \forall z\phi$$
2	1	nf5i	$$⊢Ⅎz\phi$$
3	2	nfsbv	$$⊢Ⅎz\left[y/x\right]\phi$$
4	3	nf5ri	$$⊢\left[y/x\right]\phi \to \forall z\left[y/x\right]\phi$$