Theorem frege61b

Description: Lemma for frege65b . Proposition 61 of Frege1879 p. 52. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege61b	$$⊢\left(\left[x/y\right]\phi \to \psi \right)\to \left(\forall y\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-frege58b	$$⊢\forall y\phi \to \left[x/y\right]\phi$$
2		frege9	$$⊢\left(\forall y\phi \to \left[x/y\right]\phi \right)\to \left(\left(\left[x/y\right]\phi \to \psi \right)\to \left(\forall y\phi \to \psi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\left[x/y\right]\phi \to \psi \right)\to \left(\forall y\phi \to \psi \right)$$