Metamath Proof Explorer


Theorem necon3bbii

Description: Deduction from equality to inequality. (Contributed by NM, 13-Apr-2007)

Ref Expression
Hypothesis necon3bbii.1 φ A = B
Assertion necon3bbii ¬ φ A B

Proof

Step Hyp Ref Expression
1 necon3bbii.1 φ A = B
2 1 bicomi A = B φ
3 2 necon3abii A B ¬ φ
4 3 bicomi ¬ φ A B