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Theorem ssbri 4047
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 4046 . 2 (⊤ → (𝐶𝐴𝐷𝐶𝐵𝐷))
43mptru 1362 1 (𝐶𝐴𝐷𝐶𝐵𝐷)
Colors of variables: wff set class
Syntax hints:  wi 4  wtru 1354  wss 3129   class class class wbr 4003
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142  df-br 4004
This theorem is referenced by:  brel  4678  swoer  6562  swoord1  6563  swoord2  6564  ecopover  6632  ecopoverg  6635  endom  6762
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