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

Theorem neeqtrri 2280
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtrr.1 𝐴𝐵
neeqtrr.2 𝐶 = 𝐵
Assertion
Ref Expression
neeqtrri 𝐴𝐶

Proof of Theorem neeqtrri
StepHypRef Expression
1 neeqtrr.1 . 2 𝐴𝐵
2 neeqtrr.2 . . 3 𝐶 = 𝐵
32eqcomi 2089 . 2 𝐵 = 𝐶
41, 3neeqtri 2278 1 𝐴𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1287  wne 2251
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 1379  ax-gen 1381  ax-4 1443  ax-17 1462  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-cleq 2078  df-ne 2252
This theorem is referenced by:  pnfnemnf  7463
  Copyright terms: Public domain W3C validator