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Theorem bj-prexg 10860
 Description: Proof of prexg 3974 using only bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-prexg

Proof of Theorem bj-prexg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 preq2 3478 . . . . . 6
21eleq1d 2148 . . . . 5
3 bj-zfpair2 10859 . . . . 5
42, 3vtoclg 2659 . . . 4
5 preq1 3477 . . . . 5
65eleq1d 2148 . . . 4
74, 6syl5ib 152 . . 3
87vtocleg 2670 . 2
98imp 122 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wceq 1285   wcel 1434  cvv 2602  cpr 3407 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-pr 3972  ax-bdor 10765  ax-bdeq 10769  ax-bdsep 10833 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413 This theorem is referenced by:  bj-snexg  10861  bj-unex  10868
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