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Theorem onssi 7835
Description: An ordinal number is a subset of On. (Contributed by NM, 11-Aug-1994.)
Hypothesis
Ref Expression
onssi.1 𝐴 ∈ On
Assertion
Ref Expression
onssi 𝐴 ⊆ On

Proof of Theorem onssi
StepHypRef Expression
1 onssi.1 . 2 𝐴 ∈ On
2 onss 7781 . 2 (𝐴 ∈ On → 𝐴 ⊆ On)
31, 2ax-mp 5 1 𝐴 ⊆ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2099  wss 3945  Oncon0 6363
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 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5293  ax-nul 5300  ax-pr 5423
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3or 1086  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2937  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3472  df-dif 3948  df-un 3950  df-in 3952  df-ss 3962  df-pss 3964  df-nul 4319  df-if 4525  df-pw 4600  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4904  df-br 5143  df-opab 5205  df-tr 5260  df-eprel 5576  df-po 5584  df-so 5585  df-fr 5627  df-we 5629  df-ord 6366  df-on 6367
This theorem is referenced by:  rankbnd2  9886  dfac12r  10163  cfsmolem  10287  ttukeylem6  10531
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