Theorem simplbi2

Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011)

	Ref	Expression
Hypothesis	simplbi2.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
Assertion	simplbi2	$$⊢\psi \to \left(\chi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		simplbi2.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \right)$$
2	1	biimpri	$$⊢\left(\psi \wedge \chi \right)\to \phi$$
3	2	ex	$$⊢\psi \to \left(\chi \to \phi \right)$$