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Theorem vtoclgft 3008
 Description: Closed theorem form of vtoclgf 3016. (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 2970 . 2
2 elisset 2972 . . . . 5
323ad2ant3 981 . . . 4
4 nfnfc1 2581 . . . . . . 7
5 nfcvd 2579 . . . . . . . 8
6 id 21 . . . . . . . 8
75, 6nfeqd 2592 . . . . . . 7
8 eqeq1 2448 . . . . . . . 8
98a1i 11 . . . . . . 7
104, 7, 9cbvexd 1991 . . . . . 6
1110ad2antrr 708 . . . . 5
12113adant3 978 . . . 4
133, 12mpbid 203 . . 3
14 bi1 180 . . . . . . . . 9
1514imim2i 14 . . . . . . . 8
1615com23 75 . . . . . . 7
1716imp 420 . . . . . 6
1817alanimi 1572 . . . . 5
19183ad2ant2 980 . . . 4
20 simp1r 983 . . . . 5
21 19.23t 1820 . . . . 5
2220, 21syl 16 . . . 4
2319, 22mpbid 203 . . 3
2413, 23mpd 15 . 2
251, 24syl3an3 1220 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937  wal 1550  wex 1551  wnf 1554   wceq 1653   wcel 1727  wnfc 2565  cvv 2962 This theorem is referenced by:  vtocldf  3009  riotasv2dOLD  6624 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-v 2964
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