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Theorem trel3 4303
 Description: In a transitive class, the membership relation is transitive. (Contributed by NM, 19-Apr-1994.)
Assertion
Ref Expression
trel3

Proof of Theorem trel3
StepHypRef Expression
1 3anass 940 . . 3
2 trel 4302 . . . 4
32anim2d 549 . . 3
41, 3syl5bi 209 . 2
5 trel 4302 . 2
64, 5syld 42 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wcel 1725   wtr 4295 This theorem is referenced by:  ordelord  4596 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2951  df-in 3320  df-ss 3327  df-uni 4009  df-tr 4296
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