Metamath Proof Explorer


Theorem r19.27z

Description: Restricted quantifier version of Theorem 19.27 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 r19.27z.1 x ψ
Assertion r19.27z A x A φ ψ x A φ ψ

Proof

Step Hyp Ref Expression
1 r19.27z.1 x ψ
2 r19.26 x A φ ψ x A φ x A ψ
3 1 r19.3rz A ψ x A ψ
4 3 anbi2d A x A φ ψ x A φ x A ψ
5 2 4 bitr4id A x A φ ψ x A φ ψ