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Theorem axprimlem2 4089
Description: Lemma for the primitive axioms. Primitive form of equality to a Kuratowski ordered pair. (Contributed by SF, 25-Mar-2015.)
Assertion
Ref Expression
axprimlem2
Distinct variable groups:   ,   ,,   ,   ,,   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem axprimlem2
StepHypRef Expression
1 df-opk 4058 . . 3
21eqeq2i 2363 . 2
3 dfcleq 2347 . . 3
4 vex 2862 . . . . . . 7
54elpr 3751 . . . . . 6
6 axprimlem1 4088 . . . . . . 7
7 dfcleq 2347 . . . . . . . 8
8 vex 2862 . . . . . . . . . . 11
98elpr 3751 . . . . . . . . . 10
109bibi2i 304 . . . . . . . . 9
1110albii 1566 . . . . . . . 8
127, 11bitri 240 . . . . . . 7
136, 12orbi12i 507 . . . . . 6
145, 13bitri 240 . . . . 5
1514bibi2i 304 . . . 4
1615albii 1566 . . 3
173, 16bitri 240 . 2
182, 17bitri 240 1
Colors of variables: wff set class
Syntax hints:   wb 176   wo 357  wal 1540   wceq 1642   wcel 1710  csn 3737  cpr 3738  copk 4057
This theorem is referenced by:  axxpprim  4090  axcnvprim  4091  axssetprim  4092  axsiprim  4093  axtyplowerprim  4094  axins2prim  4095  axins3prim  4096
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-sn 3741  df-pr 3742  df-opk 4058
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