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Theorem gruel 9202
 Description: Any element of an element of a Grothendieck universe is also an element of the universe. (Contributed by Mario Carneiro, 9-Jun-2013.)
Assertion
Ref Expression
gruel

Proof of Theorem gruel
StepHypRef Expression
1 gruelss 9193 . . 3
21sseld 3502 . 2
323impia 1193 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  e.wcel 1818   cgru 9189 This theorem is referenced by:  gruf  9210 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-tr 4546  df-iota 5556  df-fv 5601  df-ov 6299  df-gru 9190
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