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Theorem nancom 1300
Description: The 'nand' operator commutes. (Contributed by Mario Carneiro, 9-May-2015.)
Assertion
Ref Expression
nancom  |-  ( (
ph  -/\  ps )  <->  ( ps  -/\  ph ) )

Proof of Theorem nancom
StepHypRef Expression
1 ancom 439 . . 3  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
21notbii 289 . 2  |-  ( -.  ( ph  /\  ps ) 
<->  -.  ( ps  /\  ph ) )
3 df-nan 1298 . 2  |-  ( (
ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
4 df-nan 1298 . 2  |-  ( ( ps  -/\  ph )  <->  -.  ( ps  /\  ph ) )
52, 3, 43bitr4i 270 1  |-  ( (
ph  -/\  ps )  <->  ( ps  -/\  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    /\ wa 360    -/\ wnan 1297
This theorem is referenced by:  nanbi2  1306  falnantru  1366
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 179  df-an 362  df-nan 1298
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