Theorem exbiri

Description: Inference form of exbir . This proof is exbiriVD automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011) (Proof shortened by Wolf Lammen, 27-Jan-2013)

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

Proof

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