Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-zfpair2 Unicode version

Theorem bj-zfpair2 10417
 Description: Proof of zfpair2 3973 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 10327 . . . . 5 BOUNDED
2 ax-bdeq 10327 . . . . 5 BOUNDED
31, 2ax-bdor 10323 . . . 4 BOUNDED
4 ax-pr 3972 . . . 4
53, 4bdbm1.3ii 10398 . . 3
6 dfcleq 2050 . . . . 5
7 vex 2577 . . . . . . . 8
87elpr 3424 . . . . . . 7
98bibi2i 220 . . . . . 6
109albii 1375 . . . . 5
116, 10bitri 177 . . . 4
1211exbii 1512 . . 3
135, 12mpbir 138 . 2
1413issetri 2581 1
 Colors of variables: wff set class Syntax hints:   wb 102   wo 639  wal 1257   wceq 1259  wex 1397   wcel 1409  cvv 2574  cpr 3404 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-pr 3972  ax-bdor 10323  ax-bdeq 10327  ax-bdsep 10391 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410 This theorem is referenced by:  bj-prexg  10418
 Copyright terms: Public domain W3C validator