Metamath Proof Explorer

Theorem raleq

Description: Equality theorem for restricted universal quantifier. (Contributed by NM, 16-Nov-1995) Remove usage of ax-10 , ax-11 , and ax-12 . (Revised by Steven Nguyen, 30-Apr-2023)

Ref Expression
Assertion raleq A = B x A φ x B φ


Step Hyp Ref Expression
1 biidd A = B φ φ
2 1 raleqbi1dv A = B x A φ x B φ