Theorem pm3.14 522

Description: Theorem *3.14 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.14	⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓))

Proof of Theorem pm3.14

Step	Hyp	Ref	Expression
1		pm3.1 518	. 2 ⊢ ((𝜑 ∧ 𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓))
2	1	con2i 133	1 ⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382   ∧ wa 383

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 196  df-or 384  df-an 385

This theorem is referenced by:  naim1  31554  naim2  31555  finxpreclem2  32403  tsan2  33119  tsan3  33120  ntrneiel2  37404  onenotinotbothi  39749  twonotinotbothi  39750