Theorem frege53b

Description: Lemma for frege102 (via frege92 ). Proposition 53 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege53b	$$⊢\left[y/x\right]\phi \to \left(y=z\to \left[z/x\right]\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		frege52b	$$⊢y=z\to \left(\left[y/x\right]\phi \to \left[z/x\right]\phi \right)$$
2		ax-frege8	$$⊢\left(y=z\to \left(\left[y/x\right]\phi \to \left[z/x\right]\phi \right)\right)\to \left(\left[y/x\right]\phi \to \left(y=z\to \left[z/x\right]\phi \right)\right)$$
3	1 2	ax-mp	$$⊢\left[y/x\right]\phi \to \left(y=z\to \left[z/x\right]\phi \right)$$