Theorem 2th

Description: Two truths are equivalent. (Contributed by NM, 18-Aug-1993)

	Ref	Expression
Hypotheses	2th.1	⊢ 𝜑
	2th.2	⊢ 𝜓
Assertion	2th	⊢ ( 𝜑 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		2th.1	⊢ 𝜑
2		2th.2	⊢ 𝜓
3	2	a1i	⊢ ( 𝜑 → 𝜓 )
4	1	a1i	⊢ ( 𝜓 → 𝜑 )
5	3 4	impbii	⊢ ( 𝜑 ↔ 𝜓 )