Theorem onssi 4486

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 4464	. 2 |- ( A e. On -> A C_ On )
3	1, 2	ax-mp 5	1 |- A C_ On

Syntax hints:   e. wcel 2135   C_ wss 3111   Oncon0 4335

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-3an 969  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-ral 2447  df-rex 2448  df-v 2723  df-in 3117  df-ss 3124  df-uni 3784  df-tr 4075  df-iord 4338  df-on 4340

This theorem is referenced by: (None)