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Theorem sbcbid 2843
 Description: Formula-building deduction rule for class substitution. (Contributed by NM, 29-Dec-2014.)
Hypotheses
Ref Expression
sbcbid.1
sbcbid.2
Assertion
Ref Expression
sbcbid

Proof of Theorem sbcbid
StepHypRef Expression
1 sbcbid.1 . . . 4
2 sbcbid.2 . . . 4
31, 2abbid 2170 . . 3
43eleq2d 2123 . 2
5 df-sbc 2788 . 2
6 df-sbc 2788 . 2
74, 5, 63bitr4g 216 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102  wnf 1365   wcel 1409  cab 2042  wsbc 2787 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-sbc 2788 This theorem is referenced by:  sbcbidv  2844  csbeq2d  2902
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