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Theorem eqnetrri 2308
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 2119 . 2  |-  B  =  A
3 eqnetrr.2 . 2  |-  A  =/= 
C
42, 3eqnetri 2306 1  |-  B  =/= 
C
Colors of variables: wff set class
Syntax hints:    = wceq 1314    =/= wne 2283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-4 1470  ax-17 1489  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2284
This theorem is referenced by: (None)
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