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Metamath Proof Explorer

Theorem eqnetrri

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

Ref Expression
Hypotheses eqnetrr.1 
|- A = B
eqnetrr.2 
|- A =/= C
Assertion eqnetrri 
|- B =/= C

Proof

Step Hyp Ref Expression
1 eqnetrr.1 
 |-  A = B
2 eqnetrr.2 
 |-  A =/= C
3 1 eqcomi 
 |-  B = A
4 3 2 eqnetri 
 |-  B =/= C