Theorem pm2.76 821

Description: Theorem *2.76 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.76	⊢ ((φ ∨ (ψ → χ)) → ((φ ∨ ψ) → (φ ∨ χ)))

Proof of Theorem pm2.76

Step	Hyp	Ref	Expression
1		orimdi 820	. 2 ⊢ ((φ ∨ (ψ → χ)) ↔ ((φ ∨ ψ) → (φ ∨ χ)))
2	1	biimpi 186	1 ⊢ ((φ ∨ (ψ → χ)) → ((φ ∨ ψ) → (φ ∨ χ)))

This proof depends on syntax axioms:   → wi 4   ∨ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  pm2.75  822  pm2.81  824