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Theorem onssi 6645
Description: An ordinal number is a subset of  On. (Contributed by NM, 11-Aug-1994.)
Hypothesis
Ref Expression
onssi.1  |-  A  e.  On
Assertion
Ref Expression
onssi  |-  A  C_  On

Proof of Theorem onssi
StepHypRef Expression
1 onssi.1 . 2  |-  A  e.  On
2 onss 6599 . 2  |-  ( A  e.  On  ->  A  C_  On )
31, 2ax-mp 5 1  |-  A  C_  On
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1762    C_ wss 3471   Oncon0 4873
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-8 1764  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440  ax-sep 4563  ax-nul 4571  ax-pr 4681  ax-un 6569
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 969  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2274  df-mo 2275  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ne 2659  df-ral 2814  df-rex 2815  df-rab 2818  df-v 3110  df-sbc 3327  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-pss 3487  df-nul 3781  df-if 3935  df-sn 4023  df-pr 4025  df-tp 4027  df-op 4029  df-uni 4241  df-br 4443  df-opab 4501  df-tr 4536  df-eprel 4786  df-po 4795  df-so 4796  df-fr 4833  df-we 4835  df-ord 4876  df-on 4877
This theorem is referenced by:  rankbnd2  8278  dfac12r  8517  cfsmolem  8641  ttukeylem6  8885  nodenselem4  29009
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