Theorem 2thALT 35690

Description: Alternate proof of 2th 264. (Contributed by Hongxiu Chen, 29-Jun-2025.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
2thALT.1	⊢ 𝜑
2thALT.2	⊢ 𝜓

Assertion

Ref	Expression
2thALT	⊢ (𝜑 ↔ 𝜓)

Proof of Theorem 2thALT

Step	Hyp	Ref	Expression
1		2thALT.1	. 2 ⊢ 𝜑
2		2thALT.2	. 2 ⊢ 𝜓
3		pm5.1im 263	. 2 ⊢ (𝜑 → (𝜓 → (𝜑 ↔ 𝜓)))
4	1, 2, 3	mp2 9	1 ⊢ (𝜑 ↔ 𝜓)

Syntax hints:   ↔ wb 206

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207

This theorem is referenced by: (None)