ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl5eleqr Unicode version

Theorem syl5eleqr 2124
Description: B membership and equality inference. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl5eleqr.1
syl5eleqr.2  C
Assertion
Ref Expression
syl5eleqr  C

Proof of Theorem syl5eleqr
StepHypRef Expression
1 syl5eleqr.1 . 2
2 syl5eleqr.2 . . 3  C
32eqcomd 2042 . 2  C
41, 3syl5eleq 2123 1  C
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033
This theorem is referenced by:  rabsnt  3436  0elnn  4283  tfrexlem  5889  rdgtfr  5901  rdgruledefgg  5902
  Copyright terms: Public domain W3C validator