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Theorem sbc2ie 3220
 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 1629 . . 3
4 nfv 1629 . . 3
52nfth 1562 . . 3
6 sbc2ie.3 . . 3
73, 4, 5, 6sbc2iegf 3219 . 2
81, 2, 7mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  cvv 2948  wsbc 3153 This theorem is referenced by:  sbc3ie  3222  isprs  14379  isdrs  14383  istos  14456  rexrabdioph  26845  rmydioph  27076  rmxdioph  27078  expdiophlem2  27084 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
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