Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  elfix2 Structured version   Unicode version

Theorem elfix2 25741
 Description: Alternative membership in the fixpoint of a class. (Contributed by Scott Fenton, 11-Apr-2012.)
Hypothesis
Ref Expression
elfix2.1
Assertion
Ref Expression
elfix2

Proof of Theorem elfix2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2956 . 2
2 elfix2.1 . . 3
32brrelexi 4910 . 2
4 eleq1 2495 . . 3
5 breq12 4209 . . . 4
65anidms 627 . . 3
7 vex 2951 . . . 4
87elfix 25740 . . 3
94, 6, 8vtoclbg 3004 . 2
101, 3, 9pm5.21nii 343 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  cvv 2948   class class class wbr 4204   wrel 4875  cfix 25671 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-id 4490  df-xp 4876  df-rel 4877  df-dm 4880  df-fix 25695
 Copyright terms: Public domain W3C validator