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Theorem ssbrd 4680
 Description: Deduction from a subclass relationship of binary relations. (Contributed by NM, 30-Apr-2004.)
Hypothesis
Ref Expression
ssbrd.1 (φA B)
Assertion
Ref Expression
ssbrd (φ → (CADCBD))

Proof of Theorem ssbrd
StepHypRef Expression
1 ssbrd.1 . . 3 (φA B)
21sseld 3272 . 2 (φ → (C, D AC, D B))
3 df-br 4640 . 2 (CADC, D A)
4 df-br 4640 . 2 (CBDC, D B)
52, 3, 43imtr4g 261 1 (φ → (CADCBD))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710   ⊆ wss 3257  ⟨cop 4561   class class class wbr 4639 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-br 4640 This theorem is referenced by:  ssbri  4681  coss1  4872  coss2  4873
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