Theorem frege58bcor

Description: Lemma for frege59b . (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege58bcor	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\left[y/x\right]\phi \to \left[y/x\right]\psi \right)$$

Proof

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