Theorem expl

Description: Export a wff from a left conjunct. (Contributed by Jeff Hankins, 28-Aug-2009)

	Ref	Expression
Hypothesis	expl.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	expl	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		expl.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
2	1	exp31	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	impd	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$