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Theorem sbcbid 3206
 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 2548 . . 3
43eleq2d 2502 . 2
5 df-sbc 3154 . 2
6 df-sbc 3154 . 2
74, 5, 63bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wnf 1553   wcel 1725  cab 2421  wsbc 3153 This theorem is referenced by:  sbcbidv  3207  csbeq2d  3267 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-sbc 3154
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