Metamath Proof Explorer


Theorem necomi

Description: Inference from commutative law for inequality. (Contributed by NM, 17-Oct-2012)

Ref Expression
Hypothesis necomi.1
|- A =/= B
Assertion necomi
|- B =/= A

Proof

Step Hyp Ref Expression
1 necomi.1
 |-  A =/= B
2 necom
 |-  ( A =/= B <-> B =/= A )
3 1 2 mpbi
 |-  B =/= A