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Definition df-3nand 24834
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.)
Assertion
Ref Expression
df-3nand  |-  ( (
ph  -/\  ps  -/\  ch )  <->  (
ph  ->  ( ps  ->  -. 
ch ) ) )

Detailed syntax breakdown of Definition df-3nand
StepHypRef Expression
1 wph . . 3  wff  ph
2 wps . . 3  wff  ps
3 wch . . 3  wff  ch
41, 2, 3w3nand 24833 . 2  wff  ( ph  -/\ 
ps  -/\  ch )
53wn 3 . . . 4  wff  -.  ch
62, 5wi 4 . . 3  wff  ( ps 
->  -.  ch )
71, 6wi 4 . 2  wff  ( ph  ->  ( ps  ->  -.  ch ) )
84, 7wb 176 1  wff  ( (
ph  -/\  ps  -/\  ch )  <->  (
ph  ->  ( ps  ->  -. 
ch ) ) )
Colors of variables: wff set class
This definition is referenced by:  df3nandALT1  24835  df3nandALT2  24836  andnand1  24837
  Copyright terms: Public domain W3C validator