Theorem frege56b

Description: Lemma for frege57b . Proposition 56 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege56b	$$⊢\left(x=y\to \left(\left[x/z\right]\phi \to \left[y/z\right]\phi \right)\right)\to \left(y=x\to \left(\left[x/z\right]\phi \to \left[y/z\right]\phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		frege55b	$$⊢y=x\to x=y$$
2		frege9	$$⊢\left(y=x\to x=y\right)\to \left(\left(x=y\to \left(\left[x/z\right]\phi \to \left[y/z\right]\phi \right)\right)\to \left(y=x\to \left(\left[x/z\right]\phi \to \left[y/z\right]\phi \right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(x=y\to \left(\left[x/z\right]\phi \to \left[y/z\right]\phi \right)\right)\to \left(y=x\to \left(\left[x/z\right]\phi \to \left[y/z\right]\phi \right)\right)$$