Theorem imdistand

Description: Distribution of implication with conjunction (deduction form). (Contributed by NM, 27-Aug-2004)

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

Proof

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