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Theorem npsspw 6569
 Description: Lemma for proving existence of reals. (Contributed by Jim Kingdon, 27-Sep-2019.)
Assertion
Ref Expression
npsspw

Proof of Theorem npsspw
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 simpll 481 . . . 4
2 selpw 3366 . . . . 5
3 selpw 3366 . . . . 5
42, 3anbi12i 433 . . . 4
51, 4sylibr 137 . . 3
65ssopab2i 4014 . 2
7 df-inp 6564 . 2
8 df-xp 4351 . 2
96, 7, 83sstr4i 2984 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wb 98   wo 629   w3a 885   wcel 1393  wral 2306  wrex 2307   wss 2917  cpw 3359   class class class wbr 3764  copab 3817   cxp 4343  cnq 6378   cltq 6383  cnp 6389 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-pw 3361  df-opab 3819  df-xp 4351  df-inp 6564 This theorem is referenced by:  preqlu  6570  npex  6571  elinp  6572  prop  6573  elnp1st2nd  6574  cauappcvgprlemladd  6756
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