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Theorem opelco 5011
 Description: Ordered pair membership in a composition. (Contributed by NM, 27-Dec-1996.) (Revised by Mario Carneiro, 24-Feb-2015.)
Hypotheses
Ref Expression
opelco.1
opelco.2
Assertion
Ref Expression
opelco
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem opelco
StepHypRef Expression
1 df-br 4396 . 2
2 opelco.1 . . 3
3 opelco.2 . . 3
42, 3brco 5010 . 2
51, 4bitr3i 259 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376  wex 1671   wcel 1904  cvv 3031  cop 3965   class class class wbr 4395   ccom 4843 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-br 4396  df-opab 4455  df-co 4848 This theorem is referenced by:  dmcoss  5100  dmcosseq  5102  cotrg  5217  coiun  5352  co02  5356  coi1  5358  coass  5361  fmptco  6072  dftpos4  7010  fmptcof2  28334  cnvco1  30471  cnvco2  30472  txpss3v  30716  dffun10  30752  coiun1  36315
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