Theorem pm4.77

Description: Theorem *4.77 of WhiteheadRussell p. 121. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.77	$$⊢\left(\left(\psi \to \phi \right)\wedge \left(\chi \to \phi \right)\right)\leftrightarrow \left(\left(\psi \vee \chi \right)\to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		jaob	$$⊢\left(\left(\psi \vee \chi \right)\to \phi \right)\leftrightarrow \left(\left(\psi \to \phi \right)\wedge \left(\chi \to \phi \right)\right)$$
2	1	bicomi	$$⊢\left(\left(\psi \to \phi \right)\wedge \left(\chi \to \phi \right)\right)\leftrightarrow \left(\left(\psi \vee \chi \right)\to \phi \right)$$