Theorem 2thd

Description: Two truths are equivalent. Deduction form. (Contributed by NM, 3-Jun-2012)

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

Proof

Step	Hyp	Ref	Expression
1		2thd.1	$$⊢\phi \to \psi$$
2		2thd.2	$$⊢\phi \to \chi$$
3		pm5.1im	$$⊢\psi \to \left(\chi \to \left(\psi \leftrightarrow \chi \right)\right)$$
4	1 2 3	sylc	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$