Theorem xor3 676

Description: Two ways to express "exclusive or."

Assertion

Ref	Expression
xor3	⊢ (¬ (φ ↔ ψ) ↔ (φ ↔ ¬ ψ))

Proof of Theorem xor3

Step	Hyp	Ref	Expression
1		pm5.18 662	. . 3 ⊢ ((φ ↔ ψ) ↔ ¬ (φ ↔ ¬ ψ))
2	1	con2bii 221	. 2 ⊢ ((φ ↔ ¬ ψ) ↔ ¬ (φ ↔ ψ))
3	2	bicomi 172	1 ⊢ (¬ (φ ↔ ψ) ↔ (φ ↔ ¬ ψ))

Syntax hints:  ¬ wn 2   ↔ wb 146

This theorem is referenced by:  notzfaus 2746  nmogtmnf 8429  nmopgtmnf 9790

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

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