Metamath Proof Explorer


Theorem necon1bbii

Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007) (Proof shortened by Wolf Lammen, 24-Nov-2019)

Ref Expression
Hypothesis necon1bbii.1 ABφ
Assertion necon1bbii ¬φA=B

Proof

Step Hyp Ref Expression
1 necon1bbii.1 ABφ
2 nne ¬ABA=B
3 2 1 xchnxbi ¬φA=B