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Theorem pwtp 4014
 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 2961 . . . 4
21elpw 3807 . . 3
3 elun 3490 . . . . . 6
41elpr 3834 . . . . . . 7
51elpr 3834 . . . . . . 7
64, 5orbi12i 509 . . . . . 6
73, 6bitri 242 . . . . 5
8 elun 3490 . . . . . 6
91elpr 3834 . . . . . . 7
101elpr 3834 . . . . . . 7
119, 10orbi12i 509 . . . . . 6
128, 11bitri 242 . . . . 5
137, 12orbi12i 509 . . . 4
14 elun 3490 . . . 4
15 sstp 3965 . . . 4
1613, 14, 153bitr4ri 271 . . 3
172, 16bitri 242 . 2
1817eqriv 2435 1
 Colors of variables: wff set class Syntax hints:   wo 359   wceq 1653   wcel 1726   cun 3320   wss 3322  c0 3630  cpw 3801  csn 3816  cpr 3817  ctp 3818 This theorem is referenced by:  ex-pw  21739 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-sn 3822  df-pr 3823  df-tp 3824
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