Theorem pm3.34

Description: Theorem *3.34 (Syll) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.34	$$⊢\left(\left(\psi \to \chi \right)\wedge \left(\phi \to \psi \right)\right)\to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imim2	$$⊢\left(\psi \to \chi \right)\to \left(\left(\phi \to \psi \right)\to \left(\phi \to \chi \right)\right)$$
2	1	imp	$$⊢\left(\left(\psi \to \chi \right)\wedge \left(\phi \to \psi \right)\right)\to \left(\phi \to \chi \right)$$