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Theorem bj-zfpair2 13456
 Description: Proof of zfpair2 4170 using only bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-zfpair2

Proof of Theorem bj-zfpair2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-bdeq 13366 . . . . 5 BOUNDED
2 ax-bdeq 13366 . . . . 5 BOUNDED
31, 2ax-bdor 13362 . . . 4 BOUNDED
4 ax-pr 4169 . . . 4
53, 4bdbm1.3ii 13437 . . 3
6 dfcleq 2151 . . . . 5
7 vex 2715 . . . . . . . 8
87elpr 3581 . . . . . . 7
98bibi2i 226 . . . . . 6
109albii 1450 . . . . 5
116, 10bitri 183 . . . 4
1211exbii 1585 . . 3
135, 12mpbir 145 . 2
1413issetri 2721 1
 Colors of variables: wff set class Syntax hints:   wb 104   wo 698  wal 1333   wceq 1335  wex 1472   wcel 2128  cvv 2712  cpr 3561 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-pr 4169  ax-bdor 13362  ax-bdeq 13366  ax-bdsep 13430 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567 This theorem is referenced by:  bj-prexg  13457
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