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Theorem sbc2ie 3071
 Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 16-Dec-2008.) (Revised by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
sbc2ie.1
sbc2ie.2
sbc2ie.3
Assertion
Ref Expression
sbc2ie
Distinct variable groups:   ,,   ,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem sbc2ie
StepHypRef Expression
1 sbc2ie.1 . 2
2 sbc2ie.2 . 2
3 nfv 1609 . . 3
4 nfv 1609 . . 3
52nfth 1543 . . 3
6 sbc2ie.3 . . 3
73, 4, 5, 6sbc2iegf 3070 . 2
81, 2, 7mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1632   wcel 1696  cvv 2801  wsbc 3004 This theorem is referenced by:  sbc3ie  3073  isprs  14080  isdrs  14084  istos  14157  bisig0  26165  isibcg  26294  rexrabdioph  26978  rmydioph  27210  rmxdioph  27212  expdiophlem2  27218 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-sbc 3005
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