Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eqsbc3r Structured version   Unicode version

Theorem eqsbc3r 3210
 Description: eqsbc3 3192 with set variable on right side of equals sign. This proof was automatically generated from the virtual deduction proof eqsbc3rVD 28889 using a translation program. (Contributed by Alan Sare, 24-Oct-2011.)
Assertion
Ref Expression
eqsbc3r
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eqsbc3r
StepHypRef Expression
1 eqcom 2437 . . . . . 6
21sbcbii 3208 . . . . 5
32biimpi 187 . . . 4
4 eqsbc3 3192 . . . 4
53, 4syl5ib 211 . . 3
6 eqcom 2437 . . 3
75, 6syl6ib 218 . 2
8 idd 22 . . . . 5
98, 6syl6ibr 219 . . . 4
109, 4sylibrd 226 . . 3
1110, 2syl6ibr 219 . 2
127, 11impbid 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wsbc 3153 This theorem is referenced by:  sbcoreleleq  28556  sbcoreleleqVD  28908 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
 Copyright terms: Public domain W3C validator