Metamath Proof Explorer

Theorem neneqd

Description: Deduction eliminating inequality definition. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

Ref Expression
Hypothesis neneqd.1 
|- ( ph -> A =/= B )
Assertion neneqd 
|- ( ph -> -. A = B )

Proof

Step Hyp Ref Expression
1 neneqd.1 
 |-  ( ph -> A =/= B )
2 df-ne 
 |-  ( A =/= B <-> -. A = B )
3 1 2 sylib 
 |-  ( ph -> -. A = B )