Metamath Proof Explorer


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 )