Metamath Proof Explorer


Theorem rexeqbi1dv

Description: Equality deduction for restricted existential quantifier. (Contributed by NM, 18-Mar-1997) (Proof shortened by Steven Nguyen, 5-May-2023)

Ref Expression
Hypothesis raleqbi1dv.1 A=Bφψ
Assertion rexeqbi1dv A=BxAφxBψ

Proof

Step Hyp Ref Expression
1 raleqbi1dv.1 A=Bφψ
2 id A=BA=B
3 2 1 rexeqbidvv A=BxAφxBψ