Theorem 2thd

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

	Ref	Expression
Hypotheses	2thd.1	⊢ ( 𝜑 → 𝜓 )
	2thd.2	⊢ ( 𝜑 → 𝜒 )
Assertion	2thd	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		2thd.1	⊢ ( 𝜑 → 𝜓 )
2		2thd.2	⊢ ( 𝜑 → 𝜒 )
3		pm5.1im	⊢ ( 𝜓 → ( 𝜒 → ( 𝜓 ↔ 𝜒 ) ) )
4	1 2 3	sylc	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )