Theorem equsb3

Description: Substitution in an equality. (Contributed by Raph Levien and FL, 4-Dec-2005) Reduce axiom usage. (Revised by Wolf Lammen, 23-Jul-2023)

	Ref	Expression
Assertion	equsb3	$$⊢\left[y/x\right]x=z\leftrightarrow y=z$$

Proof

Step	Hyp	Ref	Expression
1		equequ1	$$⊢x=w\to \left(x=z\leftrightarrow w=z\right)$$
2		equequ1	$$⊢w=y\to \left(w=z\leftrightarrow y=z\right)$$
3	1 2	sbievw2	$$⊢\left[y/x\right]x=z\leftrightarrow y=z$$