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Theorem grutr 9203
 Description: A Grothendieck universe is transitive. (Contributed by Mario Carneiro, 2-Jan-2017.)
Assertion
Ref Expression
grutr

Proof of Theorem grutr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elgrug 9202 . . 3
21ibi 243 . 2
32simpld 459 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 976   wcel 1844  wral 2756  cpw 3957  cpr 3976  cuni 4193   wtr 4491   crn 4826  (class class class)co 6280   cmap 7459  cgru 9200 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-3an 978  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3063  df-dif 3419  df-un 3421  df-in 3423  df-ss 3430  df-nul 3741  df-if 3888  df-sn 3975  df-pr 3977  df-op 3981  df-uni 4194  df-br 4398  df-tr 4492  df-iota 5535  df-fv 5579  df-ov 6283  df-gru 9201 This theorem is referenced by:  gruelss  9204  gruwun  9223  intgru  9224  gruina  9228  grur1  9230  grutsk  9232
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