Theorem bj-hbsb3

Description: Shorter proof of hbsb3 . (Contributed by BJ, 2-May-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-hbsb3.1	$$⊢\phi \to \forall y\phi$$
Assertion	bj-hbsb3	$$⊢\left[y/x\right]\phi \to \forall x\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		bj-hbsb3.1	$$⊢\phi \to \forall y\phi$$
2		bj-hbsb3t	$$⊢\forall x\left(\phi \to \forall y\phi \right)\to \left(\left[y/x\right]\phi \to \forall x\left[y/x\right]\phi \right)$$
3	2 1	mpg	$$⊢\left[y/x\right]\phi \to \forall x\left[y/x\right]\phi$$