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Theorem sbcim1 3376
Description: Distribution of class substitution over implication. One direction of sbcimg 3369 that holds for proper classes. (Contributed by NM, 17-Aug-2018.)
Assertion
Ref Expression
sbcim1

Proof of Theorem sbcim1
StepHypRef Expression
1 sbcex 3337 . 2
2 sbcimg 3369 . . 3
32biimpd 207 . 2
41, 3mpcom 36 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818   cvv 3109  [.wsbc 3327
This theorem is referenced by:  sbcimdv  3396  frege59c  37949  frege60c  37950  frege62c  37952  frege65c  37955
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-or 370  df-an 371  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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