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Theorem sbc3ie 3232
 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 11 . . 3
5 sbc3ie.4 . . . 4
653expa 1154 . . 3
74, 6sbcied 3199 . 2
81, 2, 7sbc2ie 3230 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726  cvv 2958  wsbc 3163 This theorem is referenced by:  isdlat  14621  islmod  15956  rmydioph  27087  hdmap1fval  32657  hdmapfval  32690  hgmapfval  32749 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164
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