Theorem pm5.24 864

Description: Theorem *5.24 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.24	⊢ (¬ ((φ ∧ ψ) ∨ (¬ φ ∧ ¬ ψ)) ↔ ((φ ∧ ¬ ψ) ∨ (ψ ∧ ¬ φ)))

Proof of Theorem pm5.24

Step	Hyp	Ref	Expression
1		xor 861	. 2 ⊢ (¬ (φ ↔ ψ) ↔ ((φ ∧ ¬ ψ) ∨ (ψ ∧ ¬ φ)))
2		dfbi3 863	. 2 ⊢ ((φ ↔ ψ) ↔ ((φ ∧ ψ) ∨ (¬ φ ∧ ¬ ψ)))
3	1, 2	xchnxbi 299	1 ⊢ (¬ ((φ ∧ ψ) ∨ (¬ φ ∧ ¬ ψ)) ↔ ((φ ∧ ¬ ψ) ∨ (ψ ∧ ¬ φ)))

Syntax hints:  ¬ wn 3   ↔ wb 176   ∨ wo 357   ∧ wa 358

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  df-or 359  df-an 360

This theorem is referenced by: (None)