ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  eqnetrri GIF version

Theorem eqnetrri 2274
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 2087 . 2 𝐵 = 𝐴
3 eqnetrr.2 . 2 𝐴𝐶
42, 3eqnetri 2272 1 𝐵𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1285  wne 2249
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator