Theorem pm2.46 896

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 882	. 2 ⊢ (𝜓 → (𝜑 ∨ 𝜓))
2	1	con3i 155	1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ 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-or 862

This theorem is used by:  pm2.48  898  pm2.49  899  rb-ax3  1787  eueq3  3669  soasym  5592  ltnsym  11401  tglineneq  29106  expgt0b  33401  unbdqndv2lem1  37355  oexpreposd  43359  nnfoctbdjlem  47434