Theorem imdistanda

Description: Distribution of implication with conjunction (deduction version with conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011)

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

Proof

Step	Hyp	Ref	Expression
1		imdistanda.1	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
2	1	ex	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	imdistand	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \left(\psi \wedge \theta \right)\right)$$