Theorem pm2.45 386

Description: Theorem *2.45 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.45	⊢ (¬ (φ ∨ ψ) → ¬ φ)

Proof of Theorem pm2.45

Step	Hyp	Ref	Expression
1		orc 374	. 2 ⊢ (φ → (φ ∨ ψ))
2	1	con3i 127	1 ⊢ (¬ (φ ∨ ψ) → ¬ φ)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357

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 177  df-or 359

This theorem is referenced by:  pm2.47  388  dn1  932  eueq3  3012