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Theorem vtocl3gf 2917
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)
Hypotheses
Ref Expression
vtocl3gf.a
vtocl3gf.b
vtocl3gf.c
vtocl3gf.d
vtocl3gf.e
vtocl3gf.f
vtocl3gf.1
vtocl3gf.2
vtocl3gf.3
vtocl3gf.4
vtocl3gf.5
vtocl3gf.6
vtocl3gf.7
Assertion
Ref Expression
vtocl3gf

Proof of Theorem vtocl3gf
StepHypRef Expression
1 elex 2867 . . 3
2 vtocl3gf.d . . . 4
3 vtocl3gf.e . . . 4
4 vtocl3gf.f . . . 4
5 vtocl3gf.b . . . . . 6
65nfel1 2499 . . . . 5
7 vtocl3gf.2 . . . . 5
86, 7nfim 1813 . . . 4
9 vtocl3gf.c . . . . . 6
109nfel1 2499 . . . . 5
11 vtocl3gf.3 . . . . 5
1210, 11nfim 1813 . . . 4
13 vtocl3gf.5 . . . . 5
1413imbi2d 307 . . . 4
15 vtocl3gf.6 . . . . 5
1615imbi2d 307 . . . 4
17 vtocl3gf.a . . . . 5
18 vtocl3gf.1 . . . . 5
19 vtocl3gf.4 . . . . 5
20 vtocl3gf.7 . . . . 5
2117, 18, 19, 20vtoclgf 2913 . . . 4
222, 3, 4, 8, 12, 14, 16, 21vtocl2gf 2916 . . 3
231, 22mpan9 455 . 2
24233impb 1147 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wnf 1544   wceq 1642   wcel 1710  wnfc 2476  cvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  vtocl3gaf  2923
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