Theorem frege57b

Description: Analogue of frege57aid . Proposition 57 of Frege1879 p. 51. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege57b	$$⊢x=y\to \left(\left[y/z\right]\phi \to \left[x/z\right]\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		frege52b	$$⊢y=x\to \left(\left[y/z\right]\phi \to \left[x/z\right]\phi \right)$$
2		frege56b	$$⊢\left(y=x\to \left(\left[y/z\right]\phi \to \left[x/z\right]\phi \right)\right)\to \left(x=y\to \left(\left[y/z\right]\phi \to \left[x/z\right]\phi \right)\right)$$
3	1 2	ax-mp	$$⊢x=y\to \left(\left[y/z\right]\phi \to \left[x/z\right]\phi \right)$$