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Theorem strfvssn 12011
 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.) (Revised by Jim Kingdon, 19-Jan-2023.)
Hypotheses
Ref Expression
strfvssn.c Slot
strfvssn.s
strfvssn.n
Assertion
Ref Expression
strfvssn

Proof of Theorem strfvssn
StepHypRef Expression
1 strfvssn.c . . 3 Slot
2 strfvssn.s . . 3
3 strfvssn.n . . 3
41, 2, 3strnfvnd 12009 . 2
53elexd 2700 . . 3
6 fvssunirng 5440 . . 3
75, 6syl 14 . 2
84, 7eqsstrd 3134 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332   wcel 1481  cvv 2687   wss 3072  cuni 3740   crn 4544  cfv 5127  cn 8740  Slot cslot 11988 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-13 1492  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4050  ax-pow 4102  ax-pr 4135  ax-un 4359 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2689  df-sbc 2911  df-un 3076  df-in 3078  df-ss 3085  df-pw 3513  df-sn 3534  df-pr 3535  df-op 3537  df-uni 3741  df-br 3934  df-opab 3994  df-mpt 3995  df-id 4219  df-xp 4549  df-rel 4550  df-cnv 4551  df-co 4552  df-dm 4553  df-rn 4554  df-iota 5092  df-fun 5129  df-fv 5135  df-slot 11993 This theorem is referenced by: (None)
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