Theorem intmin3 4315

Description: Under subset ordering, the intersection of a class abstraction is less than or equal to any of its members. (Contributed by NM, 3-Jul-2005.)

Hypotheses

Ref	Expression
intmin3.2
intmin3.3

Assertion

Ref	Expression
intmin3

Distinct variable groups:   ,   ,

Proof of Theorem intmin3

Step	Hyp	Ref	Expression
1		intmin3.3	. . 3
2		intmin3.2	. . . 4
3	2	elabg 3247	. . 3
4	1, 3	mpbiri 233	. 2
5		intss1 4301	. 2
6	4, 5	syl 16	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  {cab 2442  C_wss 3475  |^|cint 4286

This theorem is referenced by:  intabs  4613  intid  4710

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-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-v 3111  df-in 3482  df-ss 3489  df-int 4287