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Theorem vtoclgft 2905
 Description: Closed theorem form of vtoclgf 2913. (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 2867 . 2
2 elisset 2869 . . . . 5
323ad2ant3 978 . . . 4
4 nfnfc1 2492 . . . . . . 7
5 nfcvd 2490 . . . . . . . 8
6 id 19 . . . . . . . 8
75, 6nfeqd 2503 . . . . . . 7
8 eqeq1 2359 . . . . . . . 8
98a1i 10 . . . . . . 7
104, 7, 9cbvexd 2009 . . . . . 6
1110ad2antrr 706 . . . . 5
12113adant3 975 . . . 4
133, 12mpbid 201 . . 3
14 bi1 178 . . . . . . . . 9
1514imim2i 13 . . . . . . . 8
1615com23 72 . . . . . . 7
1716imp 418 . . . . . 6
1817alanimi 1562 . . . . 5
19183ad2ant2 977 . . . 4
20 simp1r 980 . . . . 5
21 19.23t 1800 . . . . 5
2220, 21syl 15 . . . 4
2319, 22mpbid 201 . . 3
2413, 23mpd 14 . 2
251, 24syl3an3 1217 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wal 1540  wex 1541  wnf 1544   wceq 1642   wcel 1710  wnfc 2476  cvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-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:  vtocldf  2906  iota2df  4365
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