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Theorem opi1 4720
 Description: One of the two elements in an ordered pair. (Contributed by NM, 15-Jul-1993.) (Revised by Mario Carneiro, 26-Apr-2015.) (Avoid depending on this detail.)
Hypotheses
Ref Expression
opi1.1
opi1.2
Assertion
Ref Expression
opi1

Proof of Theorem opi1
StepHypRef Expression
1 snex 4694 . . 3
21prid1 4141 . 2
3 opi1.1 . . 3
4 opi1.2 . . 3
53, 4dfop 4218 . 2
62, 5eleqtrri 2554 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1767  cvv 3118  csn 4033  cpr 4035  cop 4039 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040 This theorem is referenced by:  opth1  4726  opth  4727
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