Theorem pm2.53 362

Description: Theorem *2.53 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.53	⊢ ((φ ∨ ψ) → (¬ φ → ψ))

Proof of Theorem pm2.53

Step	Hyp	Ref	Expression
1		df-or 359	. 2 ⊢ ((φ ∨ ψ) ↔ (¬ φ → ψ))
2	1	biimpi 186	1 ⊢ ((φ ∨ ψ) → (¬ φ → ψ))

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:  jaoi  368  orel1  371  pm2.63  763  pm2.8  823  mtp-orOLD  1539  19.33b  1608  nndisjeq  4430