Metamath Proof Explorer


Theorem necon3abid

Description: Deduction from equality to inequality. (Contributed by NM, 21-Mar-2007)

Ref Expression
Hypothesis necon3abid.1 φA=Bψ
Assertion necon3abid φAB¬ψ

Proof

Step Hyp Ref Expression
1 necon3abid.1 φA=Bψ
2 df-ne AB¬A=B
3 1 notbid φ¬A=B¬ψ
4 2 3 bitrid φAB¬ψ