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Theorem tr0 4316
 Description: The empty set is transitive. (Contributed by NM, 16-Sep-1993.)
Assertion
Ref Expression
tr0

Proof of Theorem tr0
StepHypRef Expression
1 0ss 3658 . 2
2 dftr4 4310 . 2
31, 2mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wss 3322  c0 3630  cpw 3801   wtr 4305 This theorem is referenced by:  ord0  4636  tctr  7682  tc0  7689  r1tr  7705 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-uni 4018  df-tr 4306
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