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Theorem nanan 1289
Description: Write 'and' in terms of 'nand'. (Contributed by Mario Carneiro, 9-May-2015.)
Assertion
Ref Expression
nanan  |-  ( (
ph  /\  ps )  <->  -.  ( ph  -/\  ps )
)

Proof of Theorem nanan
StepHypRef Expression
1 df-nan 1288 . 2  |-  ( (
ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
21con2bii 322 1  |-  ( (
ph  /\  ps )  <->  -.  ( ph  -/\  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    /\ wa 358    -/\ wnan 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-nan 1288
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