Theorem pm5.3

Description: Theorem *5.3 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Assertion	pm5.3	$$⊢\left(\left(\phi \wedge \psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\to \left(\phi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(\phi \wedge \psi \right)\to \phi$$
2	1	biantrurd	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \leftrightarrow \left(\phi \wedge \chi \right)\right)$$
3	2	pm5.74i	$$⊢\left(\left(\phi \wedge \psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\to \left(\phi \wedge \chi \right)\right)$$