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Theorem vtoclgft 3157
Description: Closed theorem form of vtoclgf 3165. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
vtoclgft

Proof of Theorem vtoclgft
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 3118 . 2
2 elisset 3120 . . . . 5
323ad2ant3 1019 . . . 4
4 nfnfc1 2622 . . . . . . 7
5 nfcvd 2620 . . . . . . . 8
6 id 22 . . . . . . . 8
75, 6nfeqd 2626 . . . . . . 7
8 eqeq1 2461 . . . . . . . 8
98a1i 11 . . . . . . 7
104, 7, 9cbvexd 2026 . . . . . 6
1110ad2antrr 725 . . . . 5
12113adant3 1016 . . . 4
133, 12mpbid 210 . . 3
14 bi1 186 . . . . . . . . 9
1514imim2i 14 . . . . . . . 8
1615com23 78 . . . . . . 7
1716imp 429 . . . . . 6
1817alanimi 1637 . . . . 5
19183ad2ant2 1018 . . . 4
20 simp1r 1021 . . . . 5
21 19.23t 1909 . . . . 5
2220, 21syl 16 . . . 4
2319, 22mpbid 210 . . 3
2413, 23mpd 15 . 2
251, 24syl3an3 1263 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  A.wal 1393  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818  F/_wnfc 2605   cvv 3109
This theorem is referenced by:  vtocldf  3158  bj-vtoclgfALT  34588
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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