Theorem intv 4253

Description: The intersection of the universal class is empty. (Contributed by NM, 11-Sep-2008.)

Assertion

Ref	Expression
intv	|- |^| _V = (/)

Proof of Theorem intv

Step	Hyp	Ref	Expression
1		0ex 4210	. 2 |- (/) e. _V
2		int0el 3952	. 2 |- ( (/) e. _V -> |^| _V = (/) )
3	1, 2	ax-mp 5	1 |- |^| _V = (/)

Syntax hints:   = wceq 1395   e. wcel 2200   _Vcvv 2799   (/)c0 3491   |^|cint 3922

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-in1 617  ax-in2 618  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-nul 4209

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-dif 3199  df-in 3203  df-ss 3210  df-nul 3492  df-int 3923

This theorem is referenced by: (None)