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Theorem strfvss 13166
 Description: A structure component extractor produces a value which is contained in a set dependent on , but not . This is sometimes useful for showing sethood. (Contributed by Mario Carneiro, 15-Aug-2015.)
Hypothesis
Ref Expression
ndxarg.1 Slot
Assertion
Ref Expression
strfvss

Proof of Theorem strfvss
StepHypRef Expression
1 fvssunirn 5551 . . 3
2 ndxarg.1 . . . . 5 Slot
3 id 19 . . . . 5
42, 3strfvnd 13163 . . . 4
54sseq1d 3205 . . 3
61, 5mpbiri 224 . 2
7 0ss 3483 . . 3
8 fvprc 5519 . . . 4
98sseq1d 3205 . . 3
107, 9mpbiri 224 . 2
116, 10pm2.61i 156 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1623   wcel 1684  cvv 2788   wss 3152  c0 3455  cuni 3827   crn 4690  cfv 5255  Slot cslot 13147 This theorem is referenced by:  wunstr  13167  prdsval  13355  prdsbas  13357  prdsplusg  13358  prdsmulr  13359  prdsvsca  13360  prdshom  13366 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-iota 5219  df-fun 5257  df-fv 5263  df-slot 13152
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