Theorem pm3.12

Description: Theorem *3.12 of WhiteheadRussell p. 111. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.12	⊢ ( ( ¬ 𝜑 ∨ ¬ 𝜓 ) ∨ ( 𝜑 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.11	⊢ ( ¬ ( ¬ 𝜑 ∨ ¬ 𝜓 ) → ( 𝜑 ∧ 𝜓 ) )
2	1	orri	⊢ ( ( ¬ 𝜑 ∨ ¬ 𝜓 ) ∨ ( 𝜑 ∧ 𝜓 ) )