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Theorem ssbri 4681
 Description: Inference from a subclass relationship of binary relations. (The proof was shortened by Andrew Salmon, 9-Jul-2011.) (Contributed by NM, 28-Mar-2007.) (Revised by set.mm contributors, 9-Jul-2011.)
Hypothesis
Ref Expression
ssbri.1
Assertion
Ref Expression
ssbri

Proof of Theorem ssbri
StepHypRef Expression
1 ssid 3290 . 2
2 ssbri.1 . . . 4
32a1i 10 . . 3
43ssbrd 4680 . 2
51, 4ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wss 3257   class class class wbr 4639 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  brel  4830
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