Metamath Proof Explorer

Theorem notbinot1

Description: Simplification rule of negation across a biconditional. (Contributed by Giovanni Mascellani, 15-Sep-2017)

Ref Expression
Assertion notbinot1 ( ¬ ( ¬ 𝜑 ↔ 𝜓 ) ↔ ( 𝜑 ↔ 𝜓 ) )

Proof

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