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Theorem elvvv 4929
 Description: Membership in universal class of ordered triples. (Contributed by NM, 17-Dec-2008.)
Assertion
Ref Expression
elvvv
Distinct variable group:   ,,,

Proof of Theorem elvvv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elxp 4887 . 2
2 anass 631 . . . . 5
3 19.42vv 1930 . . . . . 6
4 ancom 438 . . . . . . 7
542exbii 1593 . . . . . 6
6 vex 2951 . . . . . . . 8
76biantru 492 . . . . . . 7
8 elvv 4928 . . . . . . . 8
98anbi2i 676 . . . . . . 7
107, 9bitr3i 243 . . . . . 6
113, 5, 103bitr4ri 270 . . . . 5
122, 11bitr3i 243 . . . 4
13122exbii 1593 . . 3
14 exrot4 1760 . . . 4
15 excom 1756 . . . . . 6
16 opex 4419 . . . . . . . 8
17 opeq1 3976 . . . . . . . . 9
1817eqeq2d 2446 . . . . . . . 8
1916, 18ceqsexv 2983 . . . . . . 7
2019exbii 1592 . . . . . 6
2115, 20bitri 241 . . . . 5
22212exbii 1593 . . . 4
2314, 22bitr3i 243 . . 3
2413, 23bitri 241 . 2
251, 24bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  cvv 2948  cop 3809   cxp 4868 This theorem is referenced by:  ssrelrel  4968  dftpos3  6489 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-xp 4876
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