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Theorem pwtp 4242
 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 selpw 4017 . . 3
2 elun 3645 . . . . . 6
3 vex 3116 . . . . . . . 8
43elpr 4045 . . . . . . 7
53elpr 4045 . . . . . . 7
64, 5orbi12i 521 . . . . . 6
72, 6bitri 249 . . . . 5
8 elun 3645 . . . . . 6
93elpr 4045 . . . . . . 7
103elpr 4045 . . . . . . 7
119, 10orbi12i 521 . . . . . 6
128, 11bitri 249 . . . . 5
137, 12orbi12i 521 . . . 4
14 elun 3645 . . . 4
15 sstp 4191 . . . 4
1613, 14, 153bitr4ri 278 . . 3
171, 16bitri 249 . 2
1817eqriv 2463 1
 Colors of variables: wff setvar class Syntax hints:   wo 368   wceq 1379   wcel 1767   cun 3474   wss 3476  c0 3785  cpw 4010  csn 4027  cpr 4029  ctp 4031 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-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 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-ral 2819  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-pw 4012  df-sn 4028  df-pr 4030  df-tp 4032 This theorem is referenced by:  ex-pw  24827
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