Theorem onssi 4259

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

Step	Hyp	Ref	Expression
1		onssi.1	. 2 |- A e. On
2		onss 4237	. 2 |- ( A e. On -> A C_ On )
3	1, 2	ax-mp 7	1 |- A C_ On

Syntax hints:   e. wcel 1433   C_ wss 2973   Oncon0 4118

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-ral 2353  df-rex 2354  df-v 2603  df-in 2979  df-ss 2986  df-uni 3602  df-tr 3876  df-iord 4121  df-on 4123

This theorem is referenced by: (None)