Theorem pm3.1 1007

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 998	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓))
2	1	biimpi 219	1 ⊢ ((𝜑 ∧ 𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∧ wa 401   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by:  pm3.14  1011