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