MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eqnetrri Structured version   Visualization version   GIF version

Theorem eqnetrri 3017
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 2749 . 2 𝐵 = 𝐴
3 eqnetrr.2 . 2 𝐴𝐶
42, 3eqnetri 3016 1 𝐵𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wne 2945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-9 2120  ax-ext 2711
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1787  df-cleq 2732  df-ne 2946
This theorem is referenced by:  ballotlemii  32466  bj-2upln1upl  35210  sn-0tie0  40418  wallispilem4  43580
  Copyright terms: Public domain W3C validator