Theorem bnj1219

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

	Ref	Expression
Hypotheses	bnj1219.1	$$⊢\chi \leftrightarrow \left(\phi \wedge \psi \wedge \zeta \right)$$
	bnj1219.2	$$⊢\theta \leftrightarrow \left(\chi \wedge \tau \wedge \eta \right)$$
Assertion	bnj1219	$$⊢\theta \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1219.1	$$⊢\chi \leftrightarrow \left(\phi \wedge \psi \wedge \zeta \right)$$
2		bnj1219.2	$$⊢\theta \leftrightarrow \left(\chi \wedge \tau \wedge \eta \right)$$
3	1	simp2bi	$$⊢\chi \to \psi$$
4	2 3	bnj835	$$⊢\theta \to \psi$$