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Theorem eqnetrri 3085
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
eqnetrr.1 𝐴 = 𝐵
eqnetrr.2 𝐴𝐶
Assertion
Ref Expression
eqnetrri 𝐵𝐶

Proof of Theorem eqnetrri
StepHypRef Expression
1 eqnetrr.1 . . 3 𝐴 = 𝐵
21eqcomi 2833 . 2 𝐵 = 𝐴
3 eqnetrr.2 . 2 𝐴𝐶
42, 3eqnetri 3084 1 𝐵𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  wne 3014
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2817  df-ne 3015
This theorem is referenced by:  ballotlemii  31846  bj-2upln1upl  34432  wallispilem4  42663
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