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Theorem pwtp 3884
 Description: The power set of an unordered triple. (Contributed by Mario Carneiro, 2-Jul-2016.)
Assertion
Ref Expression
pwtp

Proof of Theorem pwtp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2862 . . . 4
21elpw 3728 . . 3
3 elun 3220 . . . . . 6
41elpr 3751 . . . . . . 7
51elpr 3751 . . . . . . 7
64, 5orbi12i 507 . . . . . 6
73, 6bitri 240 . . . . 5
8 elun 3220 . . . . . 6
91elpr 3751 . . . . . . 7
101elpr 3751 . . . . . . 7
119, 10orbi12i 507 . . . . . 6
128, 11bitri 240 . . . . 5
137, 12orbi12i 507 . . . 4
14 elun 3220 . . . 4
15 sstp 3870 . . . 4
1613, 14, 153bitr4ri 269 . . 3
172, 16bitri 240 . 2
1817eqriv 2350 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wceq 1642   wcel 1710   cun 3207   wss 3257  c0 3550  cpw 3722  csn 3737  cpr 3738  ctp 3739 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ne 2518  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-pw 3724  df-sn 3741  df-pr 3742  df-tp 3743 This theorem is referenced by: (None)
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