Theorem frege55lem1b

Description: Necessary deduction regarding substitution of value in equality. (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	frege55lem1b	$$⊢\left(\phi \to \left[x/y\right]y=z\right)\to \left(\phi \to x=z\right)$$

Proof

Step	Hyp	Ref	Expression
1		equsb3	$$⊢\left[x/y\right]y=z\leftrightarrow x=z$$
2	1	biimpi	$$⊢\left[x/y\right]y=z\to x=z$$
3	2	imim2i	$$⊢\left(\phi \to \left[x/y\right]y=z\right)\to \left(\phi \to x=z\right)$$