Theorem pm5.24

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

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

Proof

Step	Hyp	Ref	Expression
1		xor	⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) ↔ ( ( 𝜑 ∧ ¬ 𝜓 ) ∨ ( 𝜓 ∧ ¬ 𝜑 ) ) )
2		dfbi3	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∨ ( ¬ 𝜑 ∧ ¬ 𝜓 ) ) )
3	1 2	xchnxbi	⊢ ( ¬ ( ( 𝜑 ∧ 𝜓 ) ∨ ( ¬ 𝜑 ∧ ¬ 𝜓 ) ) ↔ ( ( 𝜑 ∧ ¬ 𝜓 ) ∨ ( 𝜓 ∧ ¬ 𝜑 ) ) )