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Theorem brrelex2i 4578
 Description: The second argument of a binary relation exists. (An artifact of our ordered pair definition.) (Contributed by Mario Carneiro, 26-Apr-2015.)
Hypothesis
Ref Expression
brrelexi.1
Assertion
Ref Expression
brrelex2i

Proof of Theorem brrelex2i
StepHypRef Expression
1 brrelexi.1 . 2
2 brrelex2 4575 . 2
31, 2mpan 420 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1480  cvv 2681   class class class wbr 3924   wrel 4539 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-xp 4540  df-rel 4541 This theorem is referenced by:  vtoclr  4582  brdomi  6636  xpdom2  6718  xpdom1g  6720  mapdom1g  6734  djudom  6971  difinfsn  6978  enomnilem  7003  djuenun  7061  aprcl  8401  hashinfom  10517  clim  11043  ntrivcvgap0  11311
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