Metamath Proof Explorer


Theorem r19.28z

Description: Restricted quantifier version of Theorem 19.28 of Margaris p. 90. It is valid only when the domain of quantification is not empty. (Contributed by NM, 26-Oct-2010)

Ref Expression
Hypothesis r19.3rz.1 x φ
Assertion r19.28z A x A φ ψ φ x A ψ

Proof

Step Hyp Ref Expression
1 r19.3rz.1 x φ
2 r19.26 x A φ ψ x A φ x A ψ
3 1 r19.3rz A φ x A φ
4 3 anbi1d A φ x A ψ x A φ x A ψ
5 2 4 bitr4id A x A φ ψ φ x A ψ