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Definition df-nor 1529
Description: Define joint denial ("not-or" or "nor"). After we define the constant true (df-tru 1544) and the constant false (df-fal 1554), we will be able to prove these truth table values: ((⊤ ⊤) ↔ ⊥) (trunortru 1590), ((⊤ ⊥) ↔ ⊥) (trunorfal 1591), ((⊥ ⊤) ↔ ⊥) (falnortru 1592), and ((⊥ ⊥) ↔ ⊤) (falnorfal 1593). Contrast with (df-an 397), (df-or 846), (wi 4), (df-nan 1490), and (df-xor 1510). (Contributed by Remi, 25-Oct-2023.)
Assertion
Ref Expression
df-nor ((𝜑 𝜓) ↔ ¬ (𝜑𝜓))

Detailed syntax breakdown of Definition df-nor
StepHypRef Expression
1 wph . . 3 wff 𝜑
2 wps . . 3 wff 𝜓
31, 2wnor 1528 . 2 wff (𝜑 𝜓)
41, 2wo 845 . . 3 wff (𝜑𝜓)
54wn 3 . 2 wff ¬ (𝜑𝜓)
63, 5wb 205 1 wff ((𝜑 𝜓) ↔ ¬ (𝜑𝜓))
Colors of variables: wff setvar class
This definition is referenced by:  norcom  1530  norcomOLD  1531  nornot  1532  noran  1533  noror  1534  norasslem1  1535  norass  1538  trunortru  1590  trunorfal  1591  falnorfal  1593  wl-df3maxtru1  36368
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