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Theorem porpss 6528
 Description: Every class is partially ordered by proper subsets. (Contributed by Stefan O'Rear, 2-Nov-2014.)
Assertion
Ref Expression
porpss []

Proof of Theorem porpss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 pssirr 3449 . . . . 5
2 psstr 3453 . . . . 5
3 vex 2961 . . . . . . . 8
43brrpss 6527 . . . . . . 7 []
54notbii 289 . . . . . 6 []
6 vex 2961 . . . . . . . . 9
76brrpss 6527 . . . . . . . 8 []
8 vex 2961 . . . . . . . . 9
98brrpss 6527 . . . . . . . 8 []
107, 9anbi12i 680 . . . . . . 7 [] []
118brrpss 6527 . . . . . . 7 []
1210, 11imbi12i 318 . . . . . 6 [] [] []
135, 12anbi12i 680 . . . . 5 [] [] [] []
141, 2, 13mpbir2an 888 . . . 4 [] [] [] []
1514rgenw 2775 . . 3 [] [] [] []
1615rgen2w 2776 . 2 [] [] [] []
17 df-po 4505 . 2 [] [] [] [] []
1816, 17mpbir 202 1 []
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wral 2707   wpss 3323   class class class wbr 4214   wpo 4503   [] crpss 6523 This theorem is referenced by:  sorpss  6529  fin23lem40  8233  isfin1-3  8268  zorng  8386 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-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-po 4505  df-xp 4886  df-rel 4887  df-rpss 6524
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