Theorem bnj835

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

	Ref	Expression
Hypotheses	bnj835.1	$$⊢\eta \leftrightarrow \left(\phi \wedge \psi \wedge \chi \right)$$
	bnj835.2	$$⊢\phi \to \tau$$
Assertion	bnj835	$$⊢\eta \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		bnj835.1	$$⊢\eta \leftrightarrow \left(\phi \wedge \psi \wedge \chi \right)$$
2		bnj835.2	$$⊢\phi \to \tau$$
3	2	3ad2ant1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \tau$$
4	1 3	sylbi	$$⊢\eta \to \tau$$