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Theorem sbcbid 2990
 Description: Formula-building deduction 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 2271 . . 3
43eleq2d 2224 . 2
5 df-sbc 2934 . 2
6 df-sbc 2934 . 2
74, 5, 63bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wnf 1437   wcel 2125  cab 2140  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-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  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-sbc 2934 This theorem is referenced by:  sbcbidv  2991  csbeq2d  3052  bezoutlemstep  11852
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