Theorem brstruct 11750

Description: The structure relation is a relation. (Contributed by Mario Carneiro, 29-Aug-2015.)

Assertion

Ref	Expression
brstruct	|- Rel Struct

Proof of Theorem brstruct

Dummy variables x f are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-struct 11743	. 2 |- Struct = { <. f , x >. | ( x e. ( <_ i^i ( NN X. NN ) ) /\ Fun ( f \ { (/) } ) /\ dom f C_ ( ... ` x ) ) }
2	1	relopabi 4603	1 |- Rel Struct

Syntax hints:   /\ w3a 930   e. wcel 1448   \ cdif 3018   i^i cin 3020   C_ wss 3021   (/)c0 3310   {csn 3474   X. cxp 4475   dom cdm 4477   Rel wrel 4482   Fun wfun 5053   ` cfv 5059   <_ cle 7673   NNcn 8578   ...cfz 9631   Struct cstr 11737

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-14 1460  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986  ax-pow 4038  ax-pr 4069

This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-rex 2381  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-pw 3459  df-sn 3480  df-pr 3481  df-op 3483  df-opab 3930  df-xp 4483  df-rel 4484  df-struct 11743

This theorem is referenced by:  isstruct2im  11751  structex  11753