Theorem bnj1254

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj1254.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \wedge \theta \wedge \tau \right)$$
Assertion	bnj1254	$$⊢\phi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		bnj1254.1	$$⊢\phi \leftrightarrow \left(\psi \wedge \chi \wedge \theta \wedge \tau \right)$$
2		id	$$⊢\tau \to \tau$$
3	2	bnj708	$$⊢\left(\psi \wedge \chi \wedge \theta \wedge \tau \right)\to \tau$$
4	1 3	sylbi	$$⊢\phi \to \tau$$