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Theorem pwnss 4367
 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 2500 . . . . . . 7
21anidms 628 . . . . . 6
32notbid 287 . . . . 5
4 df-nel 2604 . . . . . . 7
5 eleq12 2500 . . . . . . . . 9
65anidms 628 . . . . . . . 8
76notbid 287 . . . . . . 7
84, 7syl5bb 250 . . . . . 6
98cbvrabv 2957 . . . . 5
103, 9elrab2 3096 . . . 4
11 pclem6 898 . . . 4
1210, 11ax-mp 8 . . 3
13 ssel 3344 . . 3
1412, 13mtoi 172 . 2
15 ssrab2 3430 . . 3
16 elpw2g 4365 . . 3
1715, 16mpbiri 226 . 2
1814, 17nsyl3 114 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   wceq 1653   wcel 1726   wnel 2602  crab 2711   wss 3322  cpw 3801 This theorem is referenced by:  pwne  4368  pwuninel2  6546 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  ax-sep 4332 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-nel 2604  df-rab 2716  df-v 2960  df-in 3329  df-ss 3336  df-pw 3803
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