Theorem pm2.46 412

Description: Theorem *2.46 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.46	⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜓)

Proof of Theorem pm2.46

Step	Hyp	Ref	Expression
1		olc 398	. 2 ⊢ (𝜓 → (𝜑 ∨ 𝜓))
2	1	con3i 150	1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜓)

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

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 197  df-or 384

This theorem is referenced by:  pm2.48  414  pm2.49  415  rb-ax3  1719  eueq3  3414  ltnsym  10173  tglineneq  25584  soasym  31783  unbdqndv2lem1  32625  nnfoctbdjlem  40990