Theorem rabidd

Description: An "identity" law of concretion for restricted abstraction. Special case of Definition 2.1 of Quine p. 16. (Contributed by Glauco Siliprandi, 24-Jan-2025)

	Ref	Expression
Hypotheses	rabidd.1	|- ( ph -> x e. A )
	rabidd.2	|- ( ph -> ch )
Assertion	rabidd	|- ( ph -> x e. { x e. A | ch } )

Proof

Step	Hyp	Ref	Expression
1		rabidd.1	|- ( ph -> x e. A )
2		rabidd.2	|- ( ph -> ch )
3		rabid	|- ( x e. { x e. A | ch } <-> ( x e. A /\ ch ) )
4	1 2 3	sylanbrc	|- ( ph -> x e. { x e. A | ch } )