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Theorem sbciegft 3076
Description: Conversion of implicit substitution to explicit class substitution, using a bound-variable hypothesis instead of distinct variables. (Closed theorem version of sbciegf 3077.) (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
sbciegft  F/  [.  ].
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbciegft
StepHypRef Expression
1 sbc5 3070 . . 3  [.  ].
2 bi1 178 . . . . . . . 8
32imim2i 13 . . . . . . 7
43imp3a 420 . . . . . 6
54alimi 1559 . . . . 5
6 19.23t 1800 . . . . . 6  F/
76biimpa 470 . . . . 5  F/
85, 7sylan2 460 . . . 4  F/
983adant1 973 . . 3  F/
101, 9syl5bi 208 . 2  F/  [.  ].
11 bi2 189 . . . . . . . 8
1211imim2i 13 . . . . . . 7
1312com23 72 . . . . . 6
1413alimi 1559 . . . . 5
15 19.21t 1795 . . . . . 6  F/
1615biimpa 470 . . . . 5  F/
1714, 16sylan2 460 . . . 4  F/
18173adant1 973 . . 3  F/
19 sbc6g 3071 . . . 4  [.  ].
20193ad2ant1 976 . . 3  F/  [.  ].
2118, 20sylibrd 225 . 2  F/  [.  ].
2210, 21impbid 183 1  F/  [.  ].
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358   w3a 934  wal 1540  wex 1541   F/wnf 1544   wceq 1642   wcel 1710   [.wsbc 3046
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-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  df-sbc 3047
This theorem is referenced by:  sbciegf  3077  sbciedf  3081
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