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Theorem onssi 4511
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 4489 . 2 (𝐴 ∈ On → 𝐴 ⊆ On)
31, 2ax-mp 5 1 𝐴 ⊆ On
Colors of variables: wff set class
Syntax hints:  wcel 2148  wss 3129  Oncon0 4360
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2739  df-in 3135  df-ss 3142  df-uni 3808  df-tr 4099  df-iord 4363  df-on 4365
This theorem is referenced by: (None)
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