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Theorem pwnss 3912
 Description: The power set of a set is never a subset. (Contributed by Stefan O'Rear, 22-Feb-2015.)
Assertion
Ref Expression
pwnss

Proof of Theorem pwnss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq12 2102 . . . . . . 7
21anidms 377 . . . . . 6
32notbid 592 . . . . 5
4 df-nel 2207 . . . . . . 7
5 eleq12 2102 . . . . . . . . 9
65anidms 377 . . . . . . . 8
76notbid 592 . . . . . . 7
84, 7syl5bb 181 . . . . . 6
98cbvrabv 2556 . . . . 5
103, 9elrab2 2700 . . . 4
11 pclem6 1265 . . . 4
1210, 11ax-mp 7 . . 3
13 ssel 2939 . . 3
1412, 13mtoi 590 . 2
15 ssrab2 3025 . . 3
16 elpw2g 3910 . . 3
1715, 16mpbiri 157 . 2
1814, 17nsyl3 556 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wb 98   wceq 1243   wcel 1393   wnel 2205  crab 2310   wss 2917  cpw 3359 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-nel 2207  df-rab 2315  df-v 2559  df-in 2924  df-ss 2931  df-pw 3361 This theorem is referenced by:  pwne  3913  pwuninel2  5897
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