Theorem pm3.13 996

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		pm3.11 994	. 2 ⊢ (¬ (¬ 𝜑 ∨ ¬ 𝜓) → (𝜑 ∧ 𝜓))
2	1	con1i 147	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:  ifcomnan  4587  suc11  6493  nn0xmulclb  32782  naim1  36372  naim2  36373  tsbi1  38120  vk15.4j  44526  vk15.4jVD  44912