Theorem int0el 4318

Description: The intersection of a class containing the empty set is empty. (Contributed by NM, 24-Apr-2004.)

Assertion

Ref	Expression
int0el

Proof of Theorem int0el

Step	Hyp	Ref	Expression
1		intss1 4301	. 2
2		0ss 3814	. . 3
3	2	a1i 11	. 2
4	1, 3	eqssd 3520	1

Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  C_wss 3475  c0 3784  |^|cint 4286

This theorem is referenced by:  intv  4628  inton  4940  onint0  6631  oev2  7192

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-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-int 4287