Metamath Proof Explorer


Syntax definition wrals

Description: Extend wff definition to include "all some" applied to a class, which means ps is true whenever ph is true for x in A , and there is at least one x in A where ph is true. (Contributed by David A. Wheeler, 20-Oct-2018) (Revised by David A. Wheeler, 12-Jul-2026)

Ref Expression
Assertion wrals wff ∀∃ 𝑥𝐴 ( 𝜑𝜓 )