Theorem ax10w

Description: Weak version of ax-10 from which we can prove any ax-10 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. It is an alias of hbn1w introduced for labeling consistency. (Contributed by NM, 9-Apr-2017) Use hbn1w instead. (New usage is discouraged.)

	Ref	Expression
Hypothesis	ax10w.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	ax10w	$$⊢\neg \forall x\phi \to \forall x\neg \forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		ax10w.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2	1	hbn1w	$$⊢\neg \forall x\phi \to \forall x\neg \forall x\phi$$