Theorem bj-ax12wlem

Description: A lemma used to prove a weak version of the axiom of substitution ax-12 . (Temporary comment: The general statement that ax12wlem proves.) (Contributed by BJ, 20-Mar-2020)

	Ref	Expression
Hypothesis	bj-ax12wlem.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	bj-ax12wlem	$$⊢\phi \to \left(\psi \to \forall x\left(\phi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-ax12wlem.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		ax-5	$$⊢\chi \to \forall x\chi$$
3	1 2	bj-ax12i	$$⊢\phi \to \left(\psi \to \forall x\left(\phi \to \psi \right)\right)$$