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Theorem sbcimg 2974
 Description: Distribution of class substitution over implication. (Contributed by NM, 16-Jan-2004.)
Assertion
Ref Expression
sbcimg

Proof of Theorem sbcimg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 2936 . 2
2 dfsbcq2 2936 . . 3
3 dfsbcq2 2936 . . 3
42, 3imbi12d 233 . 2
5 sbim 1930 . 2
61, 4, 5vtoclbg 2770 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332  wsb 1739   wcel 2125  wsbc 2933 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-sbc 2934 This theorem is referenced by:  sbcim1  2981  sbceqal  2988  sbc19.21g  3001  sbcssg  3499  iota4an  5147  sbcfung  5187  riotass2  5796
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