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Theorem npsspw 7374
 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 519 . . . 4
2 velpw 3550 . . . . 5
3 velpw 3550 . . . . 5
42, 3anbi12i 456 . . . 4
51, 4sylibr 133 . . 3
65ssopab2i 4236 . 2
7 df-inp 7369 . 2
8 df-xp 4589 . 2
96, 7, 83sstr4i 3169 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104   wo 698   w3a 963   wcel 2128  wral 2435  wrex 2436   wss 3102  cpw 3543   class class class wbr 3965  copab 4024   cxp 4581  cnq 7183   cltq 7188  cnp 7194 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-ext 2139 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-in 3108  df-ss 3115  df-pw 3545  df-opab 4026  df-xp 4589  df-inp 7369 This theorem is referenced by:  preqlu  7375  npex  7376  elinp  7377  prop  7378  elnp1st2nd  7379  cauappcvgprlemladd  7561
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