Theorem bnj837

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj837.1	$$⊢\eta \leftrightarrow \left(\phi \wedge \psi \wedge \chi \right)$$
	bnj837.2	$$⊢\chi \to \tau$$
Assertion	bnj837	$$⊢\eta \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		bnj837.1	$$⊢\eta \leftrightarrow \left(\phi \wedge \psi \wedge \chi \right)$$
2		bnj837.2	$$⊢\chi \to \tau$$
3	2	3ad2ant3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \tau$$
4	1 3	sylbi	$$⊢\eta \to \tau$$