Metamath Proof Explorer


Definition df-3nand

Description: The double nand. This definition allows us to express the input of three variables only being false if all three are true. (Contributed by Anthony Hart, 2-Sep-2011)

Ref Expression
Assertion df-3nand φ ψ χ φ ψ ¬ χ

Detailed syntax breakdown

Step Hyp Ref Expression
0 wph wff φ
1 wps wff ψ
2 wch wff χ
3 0 1 2 w3nand wff φ ψ χ
4 2 wn wff ¬ χ
5 1 4 wi wff ψ ¬ χ
6 0 5 wi wff φ ψ ¬ χ
7 3 6 wb wff φ ψ χ φ ψ ¬ χ