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Theorem eqnetrri 2594
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 2416 . 2  |-  B  =  A
3 eqnetrr.2 . 2  |-  A  =/= 
C
42, 3eqnetri 2592 1  |-  B  =/= 
C
Colors of variables: wff set class
Syntax hints:    = wceq 1649    =/= wne 2575
This theorem is referenced by:  ballotlemii  24722  wallispilem4  27692
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-ex 1548  df-cleq 2405  df-ne 2577
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