Theorem imim2 49

Description: A closed form of syllogism (see syl 15). Theorem *2.05 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 6-Sep-2012.)

Assertion

Ref	Expression
imim2	⊢ ((φ → ψ) → ((χ → φ) → (χ → ψ)))

Proof of Theorem imim2

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ → ψ) → (φ → ψ))
2	1	imim2d 48	1 ⊢ ((φ → ψ) → ((χ → φ) → (χ → ψ)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  syldd  61  pm3.34  569