Theorem raleqbii

Description: Equality deduction for restricted universal quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypotheses	raleqbii.1	|- A = B
	raleqbii.2	|- ( ps <-> ch )
Assertion	raleqbii	|- ( A. x e. A ps <-> A. x e. B ch )

Proof

Step	Hyp	Ref	Expression
1		raleqbii.1	|- A = B
2		raleqbii.2	|- ( ps <-> ch )
3	1	eleq2i	|- ( x e. A <-> x e. B )
4	3 2	imbi12i	|- ( ( x e. A -> ps ) <-> ( x e. B -> ch ) )
5	4	ralbii2	|- ( A. x e. A ps <-> A. x e. B ch )