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Theorem onsseli 4997
 Description: Subset is equivalent to membership or equality for ordinal numbers. (Contributed by NM, 15-Sep-1995.)
Hypotheses
Ref Expression
on.1
on.2
Assertion
Ref Expression
onsseli

Proof of Theorem onsseli
StepHypRef Expression
1 on.1 . 2
2 on.2 . 2
3 onsseleq 4924 . 2
41, 2, 3mp2an 672 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818  C_wss 3475   con0 4883 This theorem is referenced by:  cardom  8388  tskcard  9180 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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-tr 4546  df-eprel 4796  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887
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