Metamath Proof Explorer

Theorem r19.28v

Description: Restricted quantifier version of one direction of 19.28 . (The other direction holds when A is nonempty, see r19.28zv .) (Contributed by NM, 2-Apr-2004) (Proof shortened by Wolf Lammen, 17-Jun-2023)

Ref Expression
Assertion r19.28v φ x A ψ x A φ ψ


Step Hyp Ref Expression
1 id φ φ
2 1 ralrimivw φ x A φ
3 2 anim1i φ x A ψ x A φ x A ψ
4 r19.26 x A φ ψ x A φ x A ψ
5 3 4 sylibr φ x A ψ x A φ ψ