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Theorem ifpdfnan 36050
 Description: Define nand as conditional logic operator. (Contributed by RP, 20-Apr-2020.)
Assertion
Ref Expression
ifpdfnan if-

Proof of Theorem ifpdfnan
StepHypRef Expression
1 df-nan 1380 . 2
2 ifpdfan 36029 . . 3 if-
32notbii 297 . 2 if-
4 ifpnot23 36042 . . 3 if- if-
5 notfal 1474 . . . 4
6 ifpbi3 36031 . . . 4 if- if-
75, 6ax-mp 5 . . 3 if- if-
84, 7bitri 252 . 2 if- if-
91, 3, 83bitri 274 1 if-
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187   wa 370   wnan 1379  if-wif 1420   wtru 1438   wfal 1442 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-nan 1380  df-ifp 1421  df-tru 1440  df-fal 1443 This theorem is referenced by: (None)
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