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Theorem opelcn 9554
 Description: Ordered pair membership in the class of complex numbers. (Contributed by NM, 14-May-1996.) (New usage is discouraged.)
Assertion
Ref Expression
opelcn

Proof of Theorem opelcn
StepHypRef Expression
1 df-c 9546 . . 3
21eleq2i 2500 . 2
3 opelxp 4880 . 2
42, 3bitri 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   wcel 1868  cop 4002   cxp 4848  cnr 9291  cc 9538 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-9 1872  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400  ax-sep 4543  ax-nul 4552  ax-pr 4657 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-ral 2780  df-rex 2781  df-rab 2784  df-v 3083  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3910  df-sn 3997  df-pr 3999  df-op 4003  df-opab 4480  df-xp 4856  df-c 9546 This theorem is referenced by:  axicn  9575
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