NoneTrue

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NoneTrue[{$expr_1$, $expr_2$, ...}, test]

returns True if no application of test to $expr_1$, $expr_2$, ... evaluates to True.

NoneTrue[list, test, level]

returns True if no application of test to items of list at level evaluates to True.

NoneTrue[test]

gives an operator that may be applied to expressions.

Nand
Nor