Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfrel4v Unicode version

Theorem dfrel4v 5001
 Description: A relation can be expressed as the set of ordered pairs in it. (Contributed by Mario Carneiro, 16-Aug-2015.)
Assertion
Ref Expression
dfrel4v
Distinct variable group:   ,,

Proof of Theorem dfrel4v
StepHypRef Expression
1 dfrel2 5000 . 2
2 eqcom 2142 . 2
3 cnvcnv3 4999 . . 3
43eqeq2i 2151 . 2
51, 2, 43bitri 205 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1332   class class class wbr 3938  copab 3997  ccnv 4549   wrel 4555 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4055  ax-pow 4107  ax-pr 4141 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2692  df-un 3081  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539  df-pr 3540  df-op 3542  df-br 3939  df-opab 3999  df-xp 4556  df-rel 4557  df-cnv 4558 This theorem is referenced by:  dffn5im  5478
 Copyright terms: Public domain W3C validator