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Theorem eqop 4611
 Description: Express equality to an ordered pair. (Contributed by SF, 6-Jan-2015.)
Assertion
Ref Expression
eqop Phi Phi 0c
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem eqop
StepHypRef Expression
1 dfcleq 2347 . 2
2 df-op 4566 . . . . . . 7 Phi Phi 0c
32eleq2i 2417 . . . . . 6 Phi Phi 0c
4 elun 3220 . . . . . 6 Phi Phi 0c Phi Phi 0c
53, 4bitri 240 . . . . 5 Phi Phi 0c
6 abid 2341 . . . . . 6 Phi Phi
7 abid 2341 . . . . . 6 Phi 0c Phi 0c
86, 7orbi12i 507 . . . . 5 Phi Phi 0c Phi Phi 0c
95, 8bitri 240 . . . 4 Phi Phi 0c
109bibi2i 304 . . 3 Phi Phi 0c
1110albii 1566 . 2 Phi Phi 0c
121, 11bitri 240 1 Phi Phi 0c
 Colors of variables: wff setvar class Syntax hints:   wb 176   wo 357  wal 1540   wceq 1642   wcel 1710  cab 2339  wrex 2615   cun 3207  csn 3737  0cc0c 4374  cop 4561   Phi cphi 4562 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-un 3214  df-op 4566 This theorem is referenced by:  setconslem3  4733  setconslem7  4737
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