MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-nor Structured version   Visualization version   GIF version

Definition df-nor 1527
Description: Define joint denial ("not-or" or "nor"). After we define the constant true (df-tru 1542) and the constant false (df-fal 1552), we will be able to prove these truth table values: ((⊤ ⊤) ↔ ⊥) (trunortru 1588), ((⊤ ⊥) ↔ ⊥) (trunorfal 1589), ((⊥ ⊤) ↔ ⊥) (falnortru 1590), and ((⊥ ⊥) ↔ ⊤) (falnorfal 1591). Contrast with (df-an 395), (df-or 844), (wi 4), (df-nan 1488), and (df-xor 1508). (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 1526 . 2 wff (𝜑 𝜓)
41, 2wo 843 . . 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  1528  norcomOLD  1529  nornot  1530  noran  1531  noror  1532  norasslem1  1533  norass  1536  trunortru  1588  trunorfal  1589  falnorfal  1591  wl-df3maxtru1  36678
  Copyright terms: Public domain W3C validator