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Theorem xor3 346
Description: Two ways to express "exclusive or." (Contributed by NM, 1-Jan-2006.)
Assertion
Ref Expression
xor3 (¬ (φψ) ↔ (φ ↔ ¬ ψ))

Proof of Theorem xor3
StepHypRef Expression
1 pm5.18 345 . . 3 ((φψ) ↔ ¬ (φ ↔ ¬ ψ))
21con2bii 322 . 2 ((φ ↔ ¬ ψ) ↔ ¬ (φψ))
32bicomi 193 1 (¬ (φψ) ↔ (φ ↔ ¬ ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176
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 177
This theorem is referenced by:  nbbn  347  pm5.15  859  nbi2  862  mpto2  1534  mtp-xorOLD  1537
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