NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  eleq1a Unicode version

Theorem eleq1a 2422
Description: A transitive-type law relating membership and equality. (Contributed by NM, 9-Apr-1994.)
Assertion
Ref Expression
eleq1a

Proof of Theorem eleq1a
StepHypRef Expression
1 eleq1 2413 . 2
21biimprcd 216 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wceq 1642   wcel 1710
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349
This theorem is referenced by:  elex22  2870  elex2  2871  reu6  3025  disjne  3596  evennn  4506  oddnn  4507  nnadjoin  4520  phi11lem1  4595  f1o2d  5727
  Copyright terms: Public domain W3C validator