Theorem pm3.13 992

Description: Theorem *3.13 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.13	⊢ (¬ (𝜑 ∧ 𝜓) → (¬ 𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm3.13

Step	Hyp	Ref	Expression
1		pm3.11 990	. 2 ⊢ (¬ (¬ 𝜑 ∨ ¬ 𝜓) → (𝜑 ∧ 𝜓))
2	1	con1i 147	1 ⊢ (¬ (𝜑 ∧ 𝜓) → (¬ 𝜑 ∨ ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 396   ∨ wo 844

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 206  df-an 397  df-or 845

This theorem is referenced by:  ifcomnan  4515  suc11  6369  nn0xmulclb  31094  naim1  34578  naim2  34579  tsbi1  36291  vk15.4j  42148  vk15.4jVD  42534