Theorem bj-ax12v

Description: A weaker form of ax-12 and ax12v , namely the generalization over x of the latter. In this statement, all occurrences of x are bound. (Contributed by BJ, 26-Dec-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-ax12v	$$⊢\forall x\left(x=t\to \left(\phi \to \forall x\left(x=t\to \phi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax12v	$$⊢x=t\to \left(\phi \to \forall x\left(x=t\to \phi \right)\right)$$
2	1	ax-gen	$$⊢\forall x\left(x=t\to \left(\phi \to \forall x\left(x=t\to \phi \right)\right)\right)$$