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Theorem vtoclgft 3129
 Description: Closed theorem form of vtoclgf 3137. (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 3089 . 2
2 elisset 3091 . . . . 5
323ad2ant3 1028 . . . 4
4 nfnfc1 2583 . . . . . . 7
5 nfcvd 2581 . . . . . . . 8
6 id 22 . . . . . . . 8
75, 6nfeqd 2587 . . . . . . 7
8 eqeq1 2426 . . . . . . . 8
98a1i 11 . . . . . . 7
104, 7, 9cbvexd 2084 . . . . . 6
1110ad2antrr 730 . . . . 5
12113adant3 1025 . . . 4
133, 12mpbid 213 . . 3
14 biimp 196 . . . . . . . . 9
1514imim2i 16 . . . . . . . 8
1615com23 81 . . . . . . 7
1716imp 430 . . . . . 6
1817alanimi 1682 . . . . 5
19183ad2ant2 1027 . . . 4
20 simp1r 1030 . . . . 5
21 19.23t 1968 . . . . 5
2220, 21syl 17 . . . 4
2319, 22mpbid 213 . . 3
2413, 23mpd 15 . 2
251, 24syl3an3 1299 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   w3a 982  wal 1435   wceq 1437  wex 1657  wnf 1661   wcel 1872  wnfc 2566  cvv 3080 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-v 3082 This theorem is referenced by:  vtocldf  3130  bj-vtoclgfALT  31593
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