Theorem intmin2 4314

Description: Any set is the smallest of all sets that include it. (Contributed by NM, 20-Sep-2003.)

Hypothesis

Ref	Expression
intmin2.1

Assertion

Ref	Expression
intmin2

Distinct variable group:   ,

Proof of Theorem intmin2

Step	Hyp	Ref	Expression
1		rabab 3127	. . 3
2	1	inteqi 4290	. 2
3		intmin2.1	. . 3
4		intmin 4306	. . 3
5	3, 4	ax-mp 5	. 2
6	2, 5	eqtr3i 2488	1

Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  {crab 2811  cvv 3109  C_wss 3475  |^|cint 4286

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-in 3482  df-ss 3489  df-int 4287