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Theorem trel3 4505
 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 989 . . 3
2 trel 4504 . . . 4
32anim2d 569 . . 3
41, 3syl5bi 221 . 2
5 trel 4504 . 2
64, 5syld 45 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   w3a 985   wcel 1887   wtr 4497 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-v 3047  df-in 3411  df-ss 3418  df-uni 4199  df-tr 4498 This theorem is referenced by:  ordelord  5445
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