Theorem onssi 4637

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 4615	. 2 |- ( A e. On -> A C_ On )
3	1, 2	ax-mp 5	1 |- A C_ On

Syntax hints:   e. wcel 2203   C_ wss 3211   Oncon0 4484

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-3an 1007  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-ral 2525  df-rex 2526  df-v 2815  df-in 3217  df-ss 3224  df-uni 3915  df-tr 4209  df-iord 4487  df-on 4489

This theorem is referenced by: (None)