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Theorem rusbcALT 27507
 Description: A version of Russell's paradox which is proven using proper substitution. (Contributed by Andrew Salmon, 18-Jun-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
rusbcALT

Proof of Theorem rusbcALT
StepHypRef Expression
1 pm5.19 350 . . 3
2 sbcnel12g 3228 . . . 4
3 sbc8g 3128 . . . 4
4 df-nel 2570 . . . . 5
5 csbvarg 3238 . . . . . . 7
65, 5eleq12d 2472 . . . . . 6
76notbid 286 . . . . 5
84, 7syl5bb 249 . . . 4
92, 3, 83bitr3d 275 . . 3
101, 9mto 169 . 2
11 df-nel 2570 . 2
1210, 11mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wcel 1721  cab 2390   wnel 2568  cvv 2916  wsbc 3121  csb 3211 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-nel 2570  df-v 2918  df-sbc 3122  df-csb 3212
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