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Theorem sbc2ie 3403
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:   , ,   ,   , ,

Proof of Theorem sbc2ie
StepHypRef Expression
1 sbc2ie.1 . 2
2 sbc2ie.2 . 2
3 nfv 1707 . . 3
4 nfv 1707 . . 3
52nfth 1625 . . 3
6 sbc2ie.3 . . 3
73, 4, 5, 6sbc2iegf 3402 . 2
81, 2, 7mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109  [.wsbc 3327
This theorem is referenced by:  sbc3ie  3405  wrd2ind  12703  isprs  15559  isdrs  15563  istos  15665  issrg  17159  isslmd  27745  rexrabdioph  30727  rmydioph  30956  rmxdioph  30958  expdiophlem2  30964
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328
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