Metamath Proof Explorer


Theorem con1bii2

Description: A contraposition inference. (Contributed by ML, 18-Oct-2020)

Ref Expression
Hypothesis con1bii2.1 ⊢ ( ¬ 𝜑 ↔ 𝜓 )
Assertion con1bii2 ( 𝜑 ↔ ¬ 𝜓 )

Proof

Step Hyp Ref Expression
1 con1bii2.1 ⊢ ( ¬ 𝜑 ↔ 𝜓 )
2 1 con1bii ⊢ ( ¬ 𝜓 ↔ 𝜑 )
3 2 bicomi ⊢ ( 𝜑 ↔ ¬ 𝜓 )