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Theorem onssi 4186
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 4165 . 2 (A On → A ⊆ On)
31, 2ax-mp 7 1 A ⊆ On
Colors of variables: wff set class
Syntax hints:   wcel 1370  wss 2890  Oncon0 4045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-3an 873  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-ral 2285  df-rex 2286  df-v 2533  df-in 2897  df-ss 2904  df-uni 3551  df-tr 3825  df-iord 4048  df-on 4050
This theorem is referenced by: (None)
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