Theorem syl6bi

Description: A mixed syllogism inference. (Contributed by NM, 2-Jan-1994)

	Ref	Expression
Hypotheses	syl6bi.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	syl6bi.2	$$⊢\chi \to \theta$$
Assertion	syl6bi	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6bi.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		syl6bi.2	$$⊢\chi \to \theta$$
3	1	biimpd	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	3 2	syl6	$$⊢\phi \to \left(\psi \to \theta \right)$$