Theorem notbinot2 38031

Description: Commutation rule between negation and biconditional. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Assertion

Ref	Expression
notbinot2	⊢ (¬ (𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ 𝜓))

Proof of Theorem notbinot2

Step	Hyp	Ref	Expression
1		nbbn 383	. 2 ⊢ ((¬ 𝜑 ↔ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓))
2	1	bicomi 224	1 ⊢ (¬ (𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ 𝜓))

Syntax hints:  ¬ wn 3   ↔ 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:  biimpor  38032