Theorem simp2bi

Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	3simp1bi.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \wedge \theta \right)$$
Assertion	simp2bi	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		3simp1bi.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \wedge \theta \right)$$
2	1	biimpi	$$⊢\phi \to \left(\psi \wedge \chi \wedge \theta \right)$$
3	2	simp2d	$$⊢\phi \to \chi$$