Theorem frege63b

Description: Lemma for frege91 . Proposition 63 of Frege1879 p. 52. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege63b	$$⊢\left[y/x\right]\phi \to \left(\psi \to \left(\forall x\left(\phi \to \chi \right)\to \left[y/x\right]\chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		frege62b	$$⊢\left[y/x\right]\phi \to \left(\forall x\left(\phi \to \chi \right)\to \left[y/x\right]\chi \right)$$
2		frege24	$$⊢\left(\left[y/x\right]\phi \to \left(\forall x\left(\phi \to \chi \right)\to \left[y/x\right]\chi \right)\right)\to \left(\left[y/x\right]\phi \to \left(\psi \to \left(\forall x\left(\phi \to \chi \right)\to \left[y/x\right]\chi \right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left[y/x\right]\phi \to \left(\psi \to \left(\forall x\left(\phi \to \chi \right)\to \left[y/x\right]\chi \right)\right)$$