Theorem imdi 147

Description: Distributive law for implication. Compare Theorem *5.41 of [WhiteheadRussell] p. 125.

Assertion

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

Proof of Theorem imdi

Step	Hyp	Ref	Expression
1		ax-2 4	. 2 ⊢ ((φ → (ψ → χ)) → ((φ → ψ) → (φ → χ)))
2		pm2.86 63	. 2 ⊢ (((φ → ψ) → (φ → χ)) → (φ → (ψ → χ)))
3	1, 2	impbi 139	1 ⊢ ((φ → (ψ → χ)) ↔ ((φ → ψ) → (φ → χ)))

Syntax hints:   → wi 2   ↔ wb 127

This theorem is referenced by:  elimant 505

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128

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