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Theorem eqnetrri 2694
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
eqnetrr.1  |-  A  =  B
eqnetrr.2  |-  A  =/= 
C
Assertion
Ref Expression
eqnetrri  |-  B  =/= 
C

Proof of Theorem eqnetrri
StepHypRef Expression
1 eqnetrr.1 . . 3  |-  A  =  B
21eqcomi 2459 . 2  |-  B  =  A
3 eqnetrr.2 . 2  |-  A  =/= 
C
42, 3eqnetri 2693 1  |-  B  =/= 
C
Colors of variables: wff setvar class
Syntax hints:    = wceq 1443    =/= wne 2621
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-ext 2430
This theorem depends on definitions:  df-bi 189  df-cleq 2443  df-ne 2623
This theorem is referenced by:  ballotlemii  29329  ballotlemiiOLD  29367  bj-2upln1upl  31611  wallispilem4  37924
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