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Theorem 0trrel 13941
Description: The empty class is a transitive relation. (Contributed by RP, 24-Dec-2019.)
Assertion
Ref Expression
0trrel (∅ ∘ ∅) ⊆ ∅

Proof of Theorem 0trrel
StepHypRef Expression
1 co01 5811 . 2 (∅ ∘ ∅) = ∅
21eqimssi 3800 1 (∅ ∘ ∅) ⊆ ∅
Colors of variables: wff setvar class
Syntax hints:  wss 3715  c0 4058  ccom 5270
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pr 5055
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-eu 2611  df-mo 2612  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-rab 3059  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-if 4231  df-sn 4322  df-pr 4324  df-op 4328  df-br 4805  df-opab 4865  df-xp 5272  df-rel 5273  df-cnv 5274  df-co 5275
This theorem is referenced by:  trclfvcotrg  13976  ust0  22244
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