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	|- ( [ y / x ] x = z <-> y = z )

Proof

Step	Hyp	Ref	Expression
1		equequ1	|- ( x = w -> ( x = z <-> w = z ) )
2		equequ1	|- ( w = y -> ( w = z <-> y = z ) )
3	1 2	sbievw2	|- ( [ y / x ] x = z <-> y = z )