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Theorem enrex 8937
 Description: The equivalence relation for signed reals exists. (Contributed by NM, 25-Jul-1995.) (New usage is discouraged.)
Assertion
Ref Expression
enrex

Proof of Theorem enrex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 npex 8855 . . . 4
21, 1xpex 4982 . . 3
32, 2xpex 4982 . 2
4 df-enr 8926 . . 3
5 opabssxp 4942 . . 3
64, 5eqsstri 3370 . 2
73, 6ssexi 4340 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  cvv 2948  cop 3809  copab 4257   cxp 4868  (class class class)co 6073  cnp 8726   cpp 8728   cer 8733 This theorem is referenced by:  addsrpr  8942  mulsrpr  8943  ltsrpr  8944  0r  8947  1sr  8948  m1r  8949  addclsr  8950  mulclsr  8951  recexsrlem  8970 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-13 1727  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-pow 4369  ax-pr 4395  ax-un 4693  ax-inf2 7588 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-tr 4295  df-eprel 4486  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577  df-lim 4578  df-suc 4579  df-om 4838  df-xp 4876  df-ni 8741  df-nq 8781  df-np 8850  df-enr 8926
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