Theorem xor3 346

Description: Two ways to express "exclusive or." (Contributed by NM, 1-Jan-2006.)

Assertion

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

Proof of Theorem xor3

Step	Hyp	Ref	Expression
1		pm5.18 345	. . 3 ⊢ ((φ ↔ ψ) ↔ ¬ (φ ↔ ¬ ψ))
2	1	con2bii 322	. 2 ⊢ ((φ ↔ ¬ ψ) ↔ ¬ (φ ↔ ψ))
3	2	bicomi 193	1 ⊢ (¬ (φ ↔ ψ) ↔ (φ ↔ ¬ ψ))

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