Metamath Proof Explorer

Theorem neeqtri

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012)

Ref Expression
Hypotheses neeqtr.1 
|- A =/= B
neeqtr.2 
|- B = C
Assertion neeqtri 
|- A =/= C

Proof

Step Hyp Ref Expression
1 neeqtr.1 
 |-  A =/= B
2 neeqtr.2 
 |-  B = C
3 2 neeq2i 
 |-  ( A =/= B <-> A =/= C )
4 1 3 mpbi 
 |-  A =/= C