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Theorem sbc2ie 3113
 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 1619 . . 3
4 nfv 1619 . . 3
52nfth 1553 . . 3
6 sbc2ie.3 . . 3
73, 4, 5, 6sbc2iegf 3112 . 2
81, 2, 7mp2an 653 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642   wcel 1710  cvv 2859  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:  sbc3ie  3115
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