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Theorem ssbri 3972
 Description: Inference from a subclass relationship of binary relations. (Contributed by NM, 28-Mar-2007.) (Revised by Mario Carneiro, 8-Feb-2015.)
Hypothesis
Ref Expression
ssbri.1 𝐴𝐵
Assertion
Ref Expression
ssbri (𝐶𝐴𝐷𝐶𝐵𝐷)

Proof of Theorem ssbri
StepHypRef Expression
1 ssbri.1 . . . 4 𝐴𝐵
21a1i 9 . . 3 (⊤ → 𝐴𝐵)
32ssbrd 3971 . 2 (⊤ → (𝐶𝐴𝐷𝐶𝐵𝐷))
43mptru 1340 1 (𝐶𝐴𝐷𝐶𝐵𝐷)
 Colors of variables: wff set class Syntax hints:   → wi 4  ⊤wtru 1332   ⊆ wss 3071   class class class wbr 3929 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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084  df-br 3930 This theorem is referenced by:  brel  4591  swoer  6457  swoord1  6458  swoord2  6459  ecopover  6527  ecopoverg  6530  endom  6657
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