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Theorem 0trrel 14333
 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 6107 . 2 (∅ ∘ ∅) = ∅
21eqimssi 4023 1 (∅ ∘ ∅) ⊆ ∅
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3934  ∅c0 4289   ∘ ccom 5552 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791  ax-sep 5194  ax-nul 5201  ax-pr 5320 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1084  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-mo 2616  df-eu 2648  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-rab 3145  df-v 3495  df-dif 3937  df-un 3939  df-in 3941  df-ss 3950  df-nul 4290  df-if 4466  df-sn 4560  df-pr 4562  df-op 4566  df-br 5058  df-opab 5120  df-xp 5554  df-rel 5555  df-cnv 5556  df-co 5557 This theorem is referenced by:  trclfvcotrg  14368  ust0  22820
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