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Theorem sbc3ie 3115
 Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Mario Carneiro, 19-Jun-2014.) (Revised by Mario Carneiro, 29-Dec-2014.)
Hypotheses
Ref Expression
sbc3ie.1
sbc3ie.2
sbc3ie.3
sbc3ie.4
Assertion
Ref Expression
sbc3ie
Distinct variable groups:   ,,,   ,,   ,   ,,,
Allowed substitution hints:   (,,)   ()   (,)

Proof of Theorem sbc3ie
StepHypRef Expression
1 sbc3ie.1 . 2
2 sbc3ie.2 . 2
3 sbc3ie.3 . . . 4
43a1i 10 . . 3
5 sbc3ie.4 . . . 4
653expa 1151 . . 3
74, 6sbcied 3082 . 2
81, 2, 7sbc2ie 3113 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934   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: (None)
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