Theorem pm3.1

Description: Theorem *3.1 of WhiteheadRussell p. 111. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ¬ ( ¬ 𝜑 ∨ ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		anor	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ¬ ( ¬ 𝜑 ∨ ¬ 𝜓 ) )
2	1	biimpi	⊢ ( ( 𝜑 ∧ 𝜓 ) → ¬ ( ¬ 𝜑 ∨ ¬ 𝜓 ) )