Theorem imim1 70

Description: A closed form of syllogism (see syl 15). Theorem *2.06 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 25-May-2013.)

Assertion

Ref	Expression
imim1	⊢ ((φ → ψ) → ((ψ → χ) → (φ → χ)))

Proof of Theorem imim1

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ → ψ) → (φ → ψ))
2	1	imim1d 69	1 ⊢ ((φ → ψ) → ((ψ → χ) → (φ → χ)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  pm2.83  71  looinv  174  pm3.33  568  tbw-ax1  1465  moim  2250  intss  3948