Theorem ax11w

Description: Weak version of ax-11 from which we can prove any ax-11 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. Unlike ax-11 , this theorem requires that x and y be distinct i.e. are not bundled. It is an alias of alcomiw introduced for labeling consistency. (Contributed by NM, 10-Apr-2017) Use alcomiw instead. (New usage is discouraged.)

	Ref	Expression
Hypothesis	ax11w.1	$$⊢y=z\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	ax11w	$$⊢\forall x\forall y\phi \to \forall y\forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		ax11w.1	$$⊢y=z\to \left(\phi \leftrightarrow \psi \right)$$
2	1	alcomiw	$$⊢\forall x\forall y\phi \to \forall y\forall x\phi$$