Theorem pm3.33

Description: Theorem *3.33 (Syll) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.33	$$⊢\left(\left(\phi \to \psi \right)\wedge \left(\psi \to \chi \right)\right)\to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imim1	$$⊢\left(\phi \to \psi \right)\to \left(\left(\psi \to \chi \right)\to \left(\phi \to \chi \right)\right)$$
2	1	imp	$$⊢\left(\left(\phi \to \psi \right)\wedge \left(\psi \to \chi \right)\right)\to \left(\phi \to \chi \right)$$