Metamath Proof Explorer
Description: A chained equality inference for inequality. (Contributed by NM, 6-Jun-2012) (Proof shortened by Wolf Lammen, 19-Nov-2019)
|
|
Ref |
Expression |
|
Hypotheses |
eqnetrrid.1 |
|- B = A |
|
|
eqnetrrid.2 |
|- ( ph -> B =/= C ) |
|
Assertion |
eqnetrrid |
|- ( ph -> A =/= C ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
eqnetrrid.1 |
|- B = A |
2 |
|
eqnetrrid.2 |
|- ( ph -> B =/= C ) |
3 |
1
|
a1i |
|- ( ph -> B = A ) |
4 |
3 2
|
eqnetrrd |
|- ( ph -> A =/= C ) |