Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  onfrALTlem4 Structured version   Unicode version

Theorem onfrALTlem4 28629
 Description: Lemma for onfrALT 28635. (Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
onfrALTlem4
Distinct variable group:   ,

Proof of Theorem onfrALTlem4
StepHypRef Expression
1 sbcan 3203 . 2
2 vex 2959 . . . 4
3 sbcel1gv 3220 . . . 4
42, 3ax-mp 8 . . 3
5 sbceqg 3267 . . . . 5
62, 5ax-mp 8 . . . 4
7 csbing 3548 . . . . . . 7
82, 7ax-mp 8 . . . . . 6
9 csbconstg 3265 . . . . . . . 8
102, 9ax-mp 8 . . . . . . 7
11 csbvarg 3278 . . . . . . . 8
122, 11ax-mp 8 . . . . . . 7
1310, 12ineq12i 3540 . . . . . 6
148, 13eqtri 2456 . . . . 5
15 csbconstg 3265 . . . . . 6
162, 15ax-mp 8 . . . . 5
1714, 16eqeq12i 2449 . . . 4
186, 17bitri 241 . . 3
194, 18anbi12i 679 . 2
201, 19bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  cvv 2956  wsbc 3161  csb 3251   cin 3319  c0 3628 This theorem is referenced by:  onfrALTlem1  28634  onfrALTlem1VD  29002 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 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-in 3327
 Copyright terms: Public domain W3C validator