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Theorem nancom 1296
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 438 . . 3  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
21notbii 288 . 2  |-  ( -.  ( ph  /\  ps ) 
<->  -.  ( ps  /\  ph ) )
3 df-nan 1294 . 2  |-  ( (
ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
4 df-nan 1294 . 2  |-  ( ( ps  -/\  ph )  <->  -.  ( ps  /\  ph ) )
52, 3, 43bitr4i 269 1  |-  ( (
ph  -/\  ps )  <->  ( ps  -/\  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    /\ wa 359    -/\ wnan 1293
This theorem is referenced by:  nanbi2  1302  falnantru  1362
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 178  df-an 361  df-nan 1294
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