Theorem pm2.64 764

Description: Theorem *2.64 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.64	⊢ ((φ ∨ ψ) → ((φ ∨ ¬ ψ) → φ))

Proof of Theorem pm2.64

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ (φ → ((φ ∨ ψ) → φ))
2		orel2 372	. . 3 ⊢ (¬ ψ → ((φ ∨ ψ) → φ))
3	1, 2	jaoi 368	. 2 ⊢ ((φ ∨ ¬ ψ) → ((φ ∨ ψ) → φ))
4	3	com12 27	1 ⊢ ((φ ∨ ψ) → ((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: (None)