Theorem nprrel 4769

Description: No proper class is related to anything via any relation. (Contributed by Roy F. Longton, 30-Jul-2005.)

Hypotheses

Ref	Expression
nprrel.1	|- Rel R
nprrel.2	|- -. A e. _V

Assertion

Ref	Expression
nprrel	|- -. A R B

Proof of Theorem nprrel

Step	Hyp	Ref	Expression
1		nprrel.2	. 2 |- -. A e. _V
2		nprrel.1	. . 3 |- Rel R
3	2	brrelex1i 4767	. 2 |- ( A R B -> A e. _V )
4	1, 3	mto 666	1 |- -. A R B

Syntax hints:   -. wn 3   e. wcel 2200   _Vcvv 2800   class class class wbr 4086   Rel wrel 4728

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-14 2203  ax-ext 2211  ax-sep 4205  ax-pow 4262  ax-pr 4297

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rex 2514  df-v 2802  df-un 3202  df-in 3204  df-ss 3211  df-pw 3652  df-sn 3673  df-pr 3674  df-op 3676  df-br 4087  df-opab 4149  df-xp 4729  df-rel 4730

This theorem is referenced by: (None)