Theorem pm3.13 1010

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 1008	. 2 ⊢ (¬ (¬ 𝜑 ∨ ¬ 𝜓) → (𝜑 ∧ 𝜓))
2	1	con1i 148	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:  ifcomnan  4539  suc11  6465  nn0xmulclb  33345  esplyfval1  34187  naim1  37147  naim2  37148  tsbi1  39033  vk15.4j  45470  vk15.4jVD  45855