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Theorem xornan2 1371
Description: XOR implies NAND (written with the  -/\ connector). (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xornan2  |-  ( (
ph  \/_  ps )  ->  ( ph  -/\  ps )
)

Proof of Theorem xornan2
StepHypRef Expression
1 xornan 1370 . 2  |-  ( (
ph  \/_  ps )  ->  -.  ( ph  /\  ps ) )
2 df-nan 1343 . 2  |-  ( (
ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
31, 2sylibr 212 1  |-  ( (
ph  \/_  ps )  ->  ( ph  -/\  ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 369    -/\ wnan 1342    \/_ wxo 1362
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 185  df-or 370  df-an 371  df-nan 1343  df-xor 1363
This theorem is referenced by: (None)
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