Theorem imdi 352

Description: Distributive law for implication. Compare Theorem *5.41 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
imdi	⊢ ((φ → (ψ → χ)) ↔ ((φ → ψ) → (φ → χ)))

Proof of Theorem imdi

Step	Hyp	Ref	Expression
1		ax-2 7	. 2 ⊢ ((φ → (ψ → χ)) → ((φ → ψ) → (φ → χ)))
2		pm2.86 94	. 2 ⊢ (((φ → ψ) → (φ → χ)) → (φ → (ψ → χ)))
3	1, 2	impbii 180	1 ⊢ ((φ → (ψ → χ)) ↔ ((φ → ψ) → (φ → χ)))

Syntax hints:   → wi 4   ↔ wb 176

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

This theorem is referenced by:  pm5.41  353  orimdi  820