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Theorem dfxor5 36213
Description: Express exclusive-or in terms of implication and negation. Statement in [Frege1879] p. 12. (Contributed by RP, 14-Apr-2020.)
Assertion
Ref Expression
dfxor5  |-  ( (
ph  \/_  ps )  <->  -.  ( ( ph  ->  -. 
ps )  ->  -.  ( -.  ph  ->  ps ) ) )

Proof of Theorem dfxor5
StepHypRef Expression
1 dfxor4 36212 . 2  |-  ( (
ph  \/_  ps )  <->  -.  ( ( -.  ph  ->  ps )  ->  -.  ( ph  ->  -.  ps )
) )
2 con2b 335 . 2  |-  ( ( ( -.  ph  ->  ps )  ->  -.  ( ph  ->  -.  ps )
)  <->  ( ( ph  ->  -.  ps )  ->  -.  ( -.  ph  ->  ps ) ) )
31, 2xchbinx 311 1  |-  ( (
ph  \/_  ps )  <->  -.  ( ( ph  ->  -. 
ps )  ->  -.  ( -.  ph  ->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    \/_ wxo 1400
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 188  df-or 371  df-an 372  df-xor 1401
This theorem is referenced by: (None)
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