Definition df-nor 1537

Description: Define joint denial ("not-or" or "nor"). After we define the constant true ⊤ (df-tru 1551) and the constant false ⊥ (df-fal 1561), we will be able to prove these truth table values: ((⊤ ⊽ ⊤) ↔ ⊥) (trunortru 1597), ((⊤ ⊽ ⊥) ↔ ⊥) (trunorfal 1598), ((⊥ ⊽ ⊤) ↔ ⊥) (falnortru 1599), and ((⊥ ⊽ ⊥) ↔ ⊤) (falnorfal 1600). Contrast with ∧ (df-an 398), ∨ (df-or 855), → (wi 4), ⊼ (df-nan 1500), and ⊻ (df-xor 1520). (Contributed by Remi, 25-Oct-2023.)

Assertion

Ref	Expression
df-nor	⊢ ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))

Detailed syntax breakdown of Definition df-nor

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		wps	. . 3 wff 𝜓
3	1, 2	wnor 1536	. 2 wff (𝜑 ⊽ 𝜓)
4	1, 2	wo 854	. . 3 wff (𝜑 ∨ 𝜓)
5	4	wn 3	. 2 wff ¬ (𝜑 ∨ 𝜓)
6	3, 5	wb 208	1 wff ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))

This definition is referenced by:  norcom  1538  nornot  1539  noran  1540  noror  1541  norasslem1  1542  norass  1545  trunortru  1597  trunorfal  1598  falnorfal  1600  wl-df3maxtru1  37869