Theorem pm3.1 993

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

Assertion

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

Proof of Theorem pm3.1

Step	Hyp	Ref	Expression
1		anor 984	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓))
2	1	biimpi 216	1 ⊢ ((𝜑 ∧ 𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 395   ∨ wo 847

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 207  df-an 396  df-or 848

This theorem is referenced by:  pm3.14  997