Theorem ax12dgen

Description: Degenerate instance of ax-12 where bundled variables x and y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017)

	Ref	Expression
Assertion	ax12dgen	$$⊢x=x\to \left(\forall x\phi \to \forall x\left(x=x\to \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ala1	$$⊢\forall x\phi \to \forall x\left(x=x\to \phi \right)$$
2	1	a1i	$$⊢x=x\to \left(\forall x\phi \to \forall x\left(x=x\to \phi \right)\right)$$