Theorem nprrel 4665

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 4663	. 2 |- ( A R B -> A e. _V )
4	1, 3	mto 662	1 |- -. A R B

Syntax hints:   -. wn 3   e. wcel 2146   _Vcvv 2735   class class class wbr 3998   Rel wrel 4625

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 614  ax-in2 615  ax-io 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-14 2149  ax-ext 2157  ax-sep 4116  ax-pow 4169  ax-pr 4203

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-ral 2458  df-rex 2459  df-v 2737  df-un 3131  df-in 3133  df-ss 3140  df-pw 3574  df-sn 3595  df-pr 3596  df-op 3598  df-br 3999  df-opab 4060  df-xp 4626  df-rel 4627

This theorem is referenced by: (None)